find the area of the original rectangle

Question

The length of a certain rectangle is 3 less than 5 times its' width. if the rectangle's width is tripled and its length is doubled, the perimeter of the new rectangle is 92 cm greater than the original perimeter. find the area of the original rectangle.

Answer 1

Hi Rhonda, let's figure this out!

 

For the original rectangle:

 

width = w

length = 5w - 3

 

Let OP = original rectangle perimeter = 2w + 2l = 2w + 2(5w-3) = 12w - 6

 

For the new rectangle:

 

width = 3w

length = 2(5w - 3) = 10w - 6

 

Let NP = new rectangle perimeter = 2w + 2l = 2(3w) + 2(10w-6) = 26w - 12

 

Set up an equation to relate the two rectangles. The perimeter of the new rectangle is 92 cm greater than the original perimeter.

 

This looks like:

 

NP = OP + 92

26w - 12 = 12w - 6 + 92

26w  - 12 = 12w + 86

14w = 98

w = 7

 

So the dimensions of the original rectangle are:

 

width = w = 7

length = 5w -3 = 32

 

Calcullate the area of the original rectangle:

 

Area = (length)(width)

A = (7)(32)

A = 224 cm2