Question

Type the correct answer in the box. Jason builds doghouses for a pet store. Each doghouse is a wooden structure with a rectangular base that has an area of 21 square feet and a length that is 4 feet more than its width. If x represents the width of the doghouse, write an equation in the given form that can be used to determine the possible dimensions of the base of the doghouse. 

Answer 1

Width = 3 feet

Length = 7 feet

Explanation:

x represents the width of doghouse so,

Width = x

Length is 4 times more than its width

Length = x+4

Area of doghouse = 21 square feet

We know

Area of rectangle = Length * Width

21 = (x+4)*x

21 = x^2+4x

=> x^2+4x-21=0

Solving the above quadratic equation by factorization to find the value of x

x^2+7x-3x-21=0

x(x+7)-3(x+7)=0

(x+7)(x-3)=0

x+7 =0 and x-3=0

x= -7 and x =3

Since the width of rectangle can never be negative so, x=3

Width =x = 3 feet

Length = x+4 = 3+4 = 7 feet

Answer 2

Answer: (x + 7)(x - 3) = 0

width (x) = 3

length (x+4) = 7

Explanation:

Area (A) = length (l) × width (x)

21 = (x + 4) × (x)

21 = x² + 4x distributed (x) into (x + 4)

0 = x² + 4x - 21 subtracted 21 from both sides

0 = (x + 7)(x - 3) factored quadratic equation

0 = x + 7 or 0 = x - 3 applied Zero Product Property

x = -7 or x = 3 solved each equation

x = -7 is not valid because lengths cannot be negative

so x = 3

and length ... x + 4 = (3) + 4 = 7