Question

A person has a garden that has a length 10 feet

longer than the width. Set up a quadratic equation
to fi d the dimensions of the garden if its area is
119 ft.2. Solve the quadratic equation to fi d the
length and width.

Answer 1

Quadratic equation: x² + 10x - 119 = 0

Length: 17 feet

Width: 7 feet

Explanation:

length: x + 10

width: x

Area = Length * Width

119 = (x + 10) * x

119 = x² + 10x

x² + 10x - 119 = 0

x² + 10x - 119 = (x + 17)(x - 7) = 0

x + 17 = 0 and x - 7 = 0

x = -17 and x = 7

Positive length and width makes more sense...

length: -17 + 10 = -7

width: -17

length: 7 + 10 = 17

width: 7

Answer 2

The width is 7 ft

The length is 17 ft

Explanation:

width = w

length = w+10

A = l*w

119 = w*(w+10)

Distribute

119 = w^2 + 10 w

Subtract 119 from each side

0 = w^2 +10w-119

Factor

0 = ( w-7) (w+17)

Using the zero product property

0 = w-7 0 = w+17

w = 7 w = -17

Since the width cannot be negative

w =7

l = w+10

l = 17

The width is 7 ft

The length is 17 ft