Question

A rectangular pen is to contain 108 ft^2 of area. if the width is 3 feet less than the length, find the dimensions of the pen.

Answer 1

Answer:width is 9ft

Length is 12 ft

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The area of a triangle is expressed as length, L × Width, W.

Area of the rectangular pen is 108 ft^2. Therefore,

LW = 108 - - - - - - - 1

if the width is 3 feet less than the length, it means that

W = L - 3

Substituting W = L - 3 into equation 1, it becomes

L(L - 3) = 108

L^2 - 3L = 108

L^2 - 3L- 108 = 0

L^2 + 9L- 12L - 108 = 0

L(L + 9) - 12(L + 9) = 0

L - 12 = 0 or L + 9= 0

L = 12 or L = - 9

The length cannot be negative,

so Length = 12ft

W = 108/L = 108/12 = 9 ft