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A picture frame measures $12 \mathrm{cm}$ by $20 \mathrm{cm},$ and $84 \mathrm{cm}^{2}$ of picture shows. Find the width of the frame.

$3 \mathrm{cm}$

Algebra

Chapter 6

Polynomial Factorizations and Equations

Section 7

Applications of Polynomial Equations

Graphs and Statistics

Exponents and Polynomials

Equations and Inequalities

Polynomials

Missouri State University

Baylor University

Idaho State University

Lectures

06:13

A picture frame measures $…

03:14

Solve.Framing a Pictur…

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A photo is $5 \mathrm{cm}$…

01:21

The rectangular painting i…

03:01

The length of a rectangula…

03:24

The frame on a picture is …

02:23

02:06

The perimeter of a rectang…

02:49

A picture measures 10 in. …

02:38

Solve each problem.A f…

02:48

PHOTOGRAPHY. The perimeter…

03:57

03:30

Use an appropriate geometr…

01:55

A picture has a square fra…

01:12

The perimeter of a square…

03:02

A rectangular photograph i…

03:08

Framing pictures. A rectan…

01:33

Framing a picture Tessa bo…

Find the length and width …

03:07

A picture frame has a tota…

this question is asking us to find the whiff of a frame given the area of a picture frame. The area of the picture frame was given to be 84 and also given the length and with of the picture frame. So when assessing, find the width of a frame is asking for this portion here. This is still with the frame. That's what is asking for. And so where were given. It's the dimensions of the picture frame, which is a different quantity. And I do this tire come to help us illustrated problem or we have X here and X here. If we add those two up, we get two X. But we want to get this portion here. So to get that portion, we could take that two X and we're gonna have to subtract it by 20. Why? Because 20 years, the whole length of the picture frame. And then we have the next year next year and we kind of find this portion here. That's just the to access, minus total length and by the same notion. We could do that for the height here. We're gonna have to actually write those checks together minus the total distance, which is 12 were gonna separate those. We know that an area of a rectangle wishes length times with and were given the area again so we could just multiply the length times with and then just solve for X for the given quantities that we, uh, accounted for. So we have 20 minus two x times 12 minus two x is equal to 84. During distribution for healing, we're going to get 240 minus 40 x minus 24 X plus four X squared is equal to 84. Combining like terms we're gonna end up getting four X squared minus 64 X plus 1 56 and now finding the greatest common factor, we could take out a four. And when we think about a four way and that with X squared minus 16 x plus 39 zero. And now just divide four by both sides and we're gonna get X squared minus 16 X plus 39 is your zero now, Just factoring using the X meant that we have been doing We're gonna get X year X year one times 39 and negative fixing here So what times? What is you? Go to 39 and what? Plus what is it with negative 16 as it was, See here is gonna be negative. 13 and negative three. This is the three of you can see that. There you go. And now we have to do is just compute for answer for X Again. X being the with so X minus 13 and ex uh, minus tree to get a zero. Now we have access with 13 and next it's go to tree for after the words only. So which one of these eggs values would actually give us a correct answer for the With Which one is correct? Answer. Well, that's easy. Just plug both them in. So this equation here and we do that we see if we plug in, but we plug in 13 for X, so we have accessible to 13. This will give us 20 minus two times 13 which gives us 20 minus 26 which, if you go to negative six, which is a negative answer. So that doesn't work out because it's saying never having a negative answer as, ah, measurements. And, you know, measurements can be negative therefore, X X entry will be our answer. And we brought that into the same equally your minister. We actually had a positive quantity.

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