The area of the rectangle is y and the perimeter is 2y+2. What are the dimensions of the rectangle?

Question

At the bottom of the question there is a model. It is a rectangle. The width is x+5 and the length is 15. 

Answer 1

We know the dimensions in terms of x, so we can write an expression for y in terms of x.

length L = 15

width W = x+5

A = y = LW

y = 15(x+5)

y = 15x+75

 

Perimeter = 2(L+W) = 2y+2

Substitute the expressions L, W and y, then solve for x.

2[(15)+(x+5)] = 2(15x+75)+2

We can divide every term by 2:

(15)+(x+5) = (15x+75)+1

20+x = 15x+76

-56 = 14x

x = -4

 

Now you can calculate the width:

W = x + 5

W = -4+5 = 1

The dimensions are 15 x 1.

 

Check:

A = 15 = y

P = 2(15+1) = 32

2y +2 = 2(15)+2 = 32