Chapter five, 58

Question

The length of a rectangular flower garden is four times its width. If the width is increased by 4m and the length is decreased by 4m, the area will be increased by 32m^2. Find the dimensions of the original garden. 

Answer 1

Hi Lauren,

 

Let's see what we know.  I like to look sentence by sentence.

 

From the first sentence

L = length

W = width

L = 4W

 

2nd sentence

A = LW

(W+4)(L-4) = A + 32 = LW + 32

 

Since we know L=4W, let's substitute 4W for each L in the equation above

(W+4)(L-4) = LW + 32

(W+4)(4W-4) = 4WW + 32

 

Let's expand and clean this up

 

4W² + 16W - 4W - 16 = 4W² + 32

4W² + 12W - 16 = 4W² + 32

Subtracting 4W² from each side

12W - 16 = 32

12W = 48

W = 4

and then 

L = 4W = 4(4) = 16

 

The garden is 16m x 4m