00:01
In question number two, we are given here the length of a rectangle is 5 inches more than twice the number.
00:09
Take here that number be x, right? the number we take it as x, right? so the length is given as 5 inches more than twice the number.
00:20
So length will be 5 inches more than twice the number, right? 5 inches more than twice the number 2x plus 5.
00:28
And width is 4 inches less than the same number so width is given as x minus 4 4 inches less than the same number the area is given as 15 area is 15 to find out the number so we have here area is given as area is equal to length into weight right what is given as the length is 2x plus 5 times we have x minus 4 that is equal to 15 right we can solve this given equation and solve for x here.
01:03
So we get 2x pure and then minus 8x plus 5x minus 20.
01:11
That equals 15.
01:13
From here we get 2x pair minus 3x minus 35.
01:20
That equals 0.
01:22
Now we just let us solve this given equation.
01:29
So we apply in this, the method of factorization, we need some of two numbers.
01:33
So sum is equal to minus 3 and product is equal to 2 times minus 35, that is minus 70.
01:43
The two numbers are given as minus 10 and 3.
01:48
And for minus 10 and 7.
01:50
There are two numbers here we have, sum is equal to minus 3 and product is minus 70, right? so we can do now, midterm splitting here, there will be 2x square, and then we have minus 10x plus 7x minus 35 not equal 0 right so from here we get 2x here x minus 5 plus 7 we have x minus 5 not equal 0 so this further we get x minus 5 then 2x plus 7 that equal 0 we create now each factor to 0 so we get x equal to 5 or we have x equal minus 7 over 2.
02:34
Now we had the length so the length was given as 2x plus 5 right 2x plus 5.
02:45
If you use let's say x equal to minus 7 by 2 then we'll have length will be minus 7 plus 5.
02:55
That will be negative number right.
02:57
The length cannot be negative therefore we cannot take this solution.
03:00
We have x equal to 5 the solution we have the number is equal to 5.
03:07
5 is the required number, all right? we want to know question number 3 here.
03:17
In question number 3, find two consecutive positive integers.
03:21
So two consecutive positive integers are given as x and x plus 1.
03:25
They have two consecutive positive integers being here.
03:28
Such that, the square of the first decreased by 17.
03:32
Square of the first decrease by 17.
03:35
That equals four times second, four times...