a-rectangular-floor-can-be-covered-completely-with-tiles-that-each-measure-one-square-foot-the-lengt

Name: a rectangular floor can be covered completely with tiles that each measure one square foot the lengt
Uploaded: 2019-08-02
Duration: 8 min 21 s
Channel: Numerade
Description: A rectangular floor can be covered completely with tiles that each measure one square foot. The length of the floor is 1 foot longer than the width and the area is less than 56 square feet. What are the possible dimensions of the floor?

Question

A rectangular floor can be covered completely with tiles that each measure one square foot. The length of the floor is 1 foot longer than the width and the area is less than 56 square feet. What are the possible dimensions of the floor?

M S · Accepted Answer

So we have a rectangle and we know that the length of the floor is one foot longer than the wits. So wait is one foot longer than the wit. So one place, the wit, we know that the area is less than 56 square feet, so the area is less than 56. Not gonna worry about units right now, So the question for area is area equals length, times with and I want a substitute. This equation here in a thrilling so area equals one plus w. So suddenly you and I want to substitute this thing for area here. Solo one plus w times of you. It&#x27;s less than 56. So now we have an inequality. The left hand side of learned ish of you. So have W closed. W squared is less than 56. And because we have a w swear I know that we&#x27;re gonna have a try an army. Also, I&#x27;m gonna get all my numbers to one side. Well, there&#x27;s a chart 50 suit. We&#x27;re gonna have a lesson zero over here. And that way we can back there looks hand side, you know that we want them to multiply to negative 56 multiplier distant nous. And let&#x27;s try to get Nick to 56. And we know you want them to add so positively the list of backers of 56 1 in 56. So in 28 4 14 and 78 So because it&#x27;s negative, we know that only one number in each pair asked me, and I do. So we&#x27;re gonna eliminate this choice because we needed to add to one. We&#x27;re gonna eliminate this also, And this here so he knows that maybe 78 and the seventh can be negative. So this is our pair here. We&#x27;re gonna use that too. But apart our middle turn, so have W squared minus seven w plus eight w and bring down to minus 56. So a group the first to grip the 2nd 2 and then factor sir, from diverse. When we get back to out of W and we&#x27;re left with W minus seven from the cycle would get back around eight. So we&#x27;re left with W minus seven. So because this factor in this factor of the same, we know they will have w plus eight time still view minus seven is less than zero. So we have our two back tears and are in the quality. Solving is different thing solving for a regular equation, as if they were said equal to zero. It&#x27;s different because inequality gives us a range of values instead of business. That number. So what he says list, then that just means negative less than zero means negative and the only way to get a negative product. We can have this factory positive this factor b negative, and I will give us a negative product. But we also need to find if this factor one negative in this factory positive and I will also give us a negative product. So we need to solve for both of these situations here, something the 1st 1 will have W Plus eight is positive or greater than zero, and W minus seven is less than zero or negative, and then we just combine. The result does the track eight from both sides here will have w is greater than negative eighths. Then we add setting the boat sides Here you&#x27;ll have ws Listen seven. Look, John I&#x27;m relying will have negative eight impulsive seventh the W is less than seven. So to go this way and w is greater than negative bait. So you go this way. So, to shade the common area No, you is in between negative Bates and seven. So, yes, I would combine it here. But we also need to saw four second situation for a second situation is if the 1st 1 is negative and the second is positive and combined results there, So w plus eight will be negative. Listen, zero and W minus seven will be positive or greater than zero. That&#x27;s all for W. We get W. It&#x27;s less than negative. Eight. Dance off the w Here we get w is good and positive. Seven. No joking and realize will have negative eights and positive. Seven. The W is greater than seven. So to go that way and w is less than that innovates sort of it that way. And there is no common area between the suit, so there&#x27;s no way to combine our second situation here. Therefore, our answer. ISS negative eight. His list and W He&#x27;s lost 37 so it wants to know what a possible dimensions of the floor for a possible dimensions are obviously going to be in this range here that we just brute. However, we cannot have a negative wit. So our wits he&#x27;s going to be between zero in seven because we cannot have a negative. I&#x27;m gonna write that down. Cannot have negative would. So we&#x27;re gonna properly 0 to 7 feet. We also need to find a link, and we&#x27;re just gonna plug w in for Are the buttes blindly? So originally, our equation ways bill equals one plus w. And if we just plug W in our lowest w so we can plug in zero and we get one for our lowest value. We also need to find the highest value. So we have one plus in our highest valuable study. So it&#x27;s a so link is in between wine and a So here. That&#x27;s the answer is here. And you saw further possible dimensions. I&#x27;ll always remember whenever dealing with, like, a door be or anything of the sort. Remember that you cannot have a native value

Charles Carter · Answer

Okay, This one starts off by saying that the length of a rectangle it&#x27;s six inches longer than its with sweeping rally was six plus w Okay, then we know that w times L The area of the rectangle is greater than or equal to 667 square inches. So we were playing the L of six plus w into our second equation. So what l w time six plus w is greater than or equal to 667. And we can write that as W Square plus six. W, uh, minus 6 67 is greater than or equal to zero. We can factor this quadratic into W plus 29 times w minus 23. It is greater than or equal to zero. And so when it&#x27;s greater than or equal to zero w and we&#x27;re talking about a rectangle with, so we&#x27;re not gonna be working with negatives. So what is seen to make sure that W is greater than or equal to 23? Okay, so it could be less than negative 29. But then we have a negative width and length. So are with is greater than or equal to 23 which also implies that are length I would have to be greater than or equal to 29. Okay, so it only asked about the Web&#x27;s, but they have both, thank you very much.

Joseph Franks · Answer

that we&#x27;re dealing with the area around being 48. And this rectangular rug has a length of his do Morgan with, um so just setting up the equation, remember, area of a rectangle is like times with, so we&#x27;ll have 48 equals, um, two plus w since the white two. More than the way times w So this sets up a nice quadratic equation of w squared. Plus two of you, minus 48 equals zero or the W minus six. We&#x27;ll close it. So we I&#x27;m going to get w equal six on demure equals minus eight. There we can, um, emotionally, because simply they don&#x27;t exist. So with your six, and we know, um, that the life is two more than the width. So two plus, um six. Um, we will know the dimensions. The wishes of the six. The life has got to be eight

Bahar Tehranipoor · Answer

in this problem we have the width of a rectangle is 12 feet less than this length. So let&#x27;s call this the with. We&#x27;ll call this the length and we&#x27;ll say that w equals L minus 12 were also give that the area is 540. So we know the area of a rectangle just the with times length we have w l equals 5 40 Now we can just substitute in w so that we have this equation in terms about doing that We&#x27;re going to get l A. Times l minus 12 equals 5 40 Multiplying this out, we&#x27;ll get l squared minus 12 l If you subtract this 5 40 minus 5 40 equals zero. So let&#x27;s see, what can we factor this 5 40 into? We know that doing some simple calculations that 5 40 is actually a multiple of thirties. We can say that l minus or my bad plus 30. And then if we divide 5 40 by 30 it&#x27;ll be 54 over three. So 18. So if we want to get a negative 12 l will actually want to have a negative 30 here. So, huh, Negative 30 and then l plus 18. So this is a bit of a trick you&#x27;re one to find. But if you use the calculator is actually really easy. So it be 13 18 checking really quickly. Have l squared plus 18 on minus 30 out, which will give us negative about and then our minus 5 40 So, of course l cannot equal negative 18. That&#x27;s a negative length toe. All must be 30. So knowing that l is 30 you can put that back into the with so 30 minus two of his 18 and you&#x27;re with his 18.

Amrita Bhasin · Answer

this question essentially asked us to factor it X squared plus 30 x plus. So what we know we can do is we can consider a multitude of factors. For example, given 15 acts, we have eight X plus seven times X plus one, then given 18 acts we have for ex post seven times two X plus one, then given 30 X. We have two X plus seven times four X plus one. Now we have to consider the fact that everything must be positive and the two factors must be seven and one because seven is prime. Therefore, what we know is the coefficient of the ex parte must multiplies that they equal 30 axe. So this last option is the option to explosive in temps for X minus one. This is the option for which we see the length and the width of the rectangle.

Joseph Lentino · Answer

in this problem, we have a rectangle. We know that the area of the rectangle is 135 square feet. We also know that the with So if this is the link, the with is going to be six feet less than the length. So l minus six and l areas equal to length times with. So we have l times l minus six in that must equal 135 going to distribute the l. So I have l squared minus six. L and I&#x27;m also going to subtract 1 35 from both sides of the equation minus 1 35 equals zero. So the link must be a positive value. One of my values will be positive. One will be negative because I&#x27;m multiplying to get a negative number. The larger of the two night numbers will be negative. So let&#x27;s take a look at the factors of 1 35 They need to subtract 26 So one in 1 35 will be 1 34 That&#x27;s no good. Um, for nine. So three goes in, three goes in Ah, 45 times. That gives me a difference of 42. No, good. Five goes in and it goes in, um, 27 times, which has a difference of 22. No good. Ah, six does not go in. Seven does not go in eight does not going nine goes in. Nine goes in once with 45 15. The difference between 15 and nine a six. Hooray! The 15 must be the large is the larger distance away from zero So that will be negative And this will be a positive nine to get a negative six. So l equals 15 or l equals negative night with link can&#x27;t be negative Therefore, we must have 15 feet as our lank And because we&#x27;re looking for the dimensions we have to find the with which will be six less than that so 15 by six foot rectangle 15 by six feet

Problem

A carton is completely filled with boxes that are…

Problem 18 Hard Difficulty

A rectangular floor can be covered completely with tiles that each measure one square foot. The length of the floor is 1 foot longer than the width and the area is less than 56 square feet. What are the possible dimensions of the floor?

Answer

Thus the width is between 0 ft and 7 ft (because the width has to be positive) and the length is between 1 and 8 ft.

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Thus the width is between 0 ft and 7 ft (because the width has to be positive) and the length is between 1 and 8 ft.

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Heather Z.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Anna Marie V.

Heather Z.

Caleb E.

Ann Xavier Gantert

Algebra 2 and Trigonometry