A rectangular yard has an area 96 square feet. If the width of the yard is 4 feet less than the length. What is the perimeter in feet, of the yard

Question

A. 40

B. 44

C.48

D. 52

 

Answer 1

To answer this question, we need to define our variables:

W=width

L=length

W= L-4

We know our area so we can plug these variables into the area equation (LxW=Area)

We now need to solve for each variable.

96=LX(L-4)

L^2-4L=96

L^2-4L-96=0

(L+8)X(L-12)=0 You get this from factoring

You must change the signs in both parentheses to find possible solutions:

L=-8 and L=12 but you cannot have a negative length so the only solution would be L=12

Plug this into your equation for the width given in your question:

W=L-4

W=12-4

W=8

Then you take the length and width and multiply each by 2 to get the perimeter:

2(8)+2(12)=40

Answer 2

Let x = the length

Let x - 4 = the width

A = lw

96 = x(x - 4)

96 = x² - 4x

x² - 4x - 96 = 0

(x - 12)(x + 8) = 0

x - 12 = 0     or     x + 8 = 0

x = 12 feet   or     x = -8, illogical answer

x - 4 = 12 - 4 = 8 feet

 

P = 2l + 2w

P = 2(12) + 2(8)

P = 24 + 16

P = 40 feet