Variable Expressions

Question

The width of a rectangle is two thirds of the length. The perimeter of the rectangle is 15 cm. What is the length,l, of the rectangle? Explain.

Answer 1

Translate the sentence into math symbols....

 

We'll say width is "w" and length is "l" just so you can distinguish which is which.

 

 

The width of a rectangle is two thirds the length.

"The width" means   w

"is" means     =

"two thirds" means     2/3

And because we don't know how long the rectangle's length is, we'll call

that "x"

All this becomes an equation because we know it has to equal 15.

 

w = 2/3 x  and there are two sides to the rectangle that is the width.

l = x   and there are two sides to the rectangle that is the length.

And the perimeter P = 15

Put it altogether....    P = w + w + l + l

                              15 = 2/3x + 2/3x + x + x

                              15 = 10/3x

                              45 = 10x

                              4.5 = x

 

This tells us the length, x, is 4.5

and the width is 2/3 of this which is....

 

2/3 (4.5) = 3