Algebra question

Question

The length of a rectangle is 8 meters less than 5 times the width. If the perimeter of the rectangle is 104 meters, find the width of the rectangle.

Answer 1

Hello Jen,

First, let's come up with the expressions which represent the information in the problem, fair enough?

Therefore:

Let the length equal 5x - 8

Let the width equal x

Second, the equation which is for the Perimeter of a rectangle is as follows:

P = 2(L + W) or P = 2(L) + 2(W) where P equals perimeter, L equals the length, and W equals the width. You will notice that the second equation is exactly the same as the first with the distributive property of math applied. Let's use that particular equation to determine the length and width of this rectangle.

P = 2(5x - 8) + 2(x) <------This is simply the equation while substituting the length and width

104 = 10x - 16 + 2x <-------We simply have substituted the perimeter for P

104 = 12x - 16 <-------We then added 16 to both sides of the equation

120 = 12x <------We then divided both sides of the equation by 12

x = 10 <------This is the width of the rectangle

Next we want to substitute 10 for x for the expression of the length. That expression is as follows:

5x - 8 =

5(10) - 8 =

50 - 8 = 42

42 <--------This is the length in meters.

Finally, we want to check our work, okay? Remember in our answer we have 10 for the width and 42 for the length. To check our work, all we need do is substitute these values and set the equation equal to 104.

P = 2(L) + 2(W)

104 = 2(42) + 2(10)

104 = 84 + 20

104 = 104

The values check out and the solution is therefore valid. I hope this assists you and that you have a great end of the week. Please feel free to leave any feedback, seek clarity, or ask any further questions regarding this solution by clicking the "Add Comment" prompt. If you need one on one tutoring, please feel free to reach out to me or any tutor. Best!