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Question

A farmer wants to fence off a portion of a square field for a vegetable garden. The length of the garden will be 4 feet less than the length of the square field. The width of the garden will be 8 feet less than the width of the square field. If the area of the garden is 192 square feet, what are the dimensions of the garden

Answer 1

Let x=a side of the square field

Since the field is a square, x represents both the length and the width

Since the length of the garden will be 4 feet less than the length of the square field, the length of the garden is represented by (x-4)

The width of the garden is 8 less than the width of the field, so it is represented by (x-8)

Area = length * width

Area of garden = 192 ft²

Length = (x-4)

Width = (x-8)

192 = (x-4) * (x-8) Distribute

192 = x² - 8x - 4x + 32 Subtract 192 from both sides to set equation equal to 0

x² - 12x - 160 = 0 Can factor equation by grouping or use quadratic formula to solve for x

x² - 20x + 8x - 160 = 0

x * (x - 20) + 8 * (x - 20) = 0

(x + 8) * (x - 20) = 0

x + 8 = 0 x - 20 = 0

x = -8 x = 20

Reject the negative because a length or width of a garden can't be negative

x = 20

Side of square field = 20

Dimensions of the garden are:

Length = x-4 = 20 - 4 = 16

Width = x-8 = 20 - 8 = 12

The dimensions of the garden are 16ft x 12ft

Answer 2

s: length of the side of the field

(s-4)(s-8)=192

s^2-12s+32=192

s^2-12s+160=0

(s-20)(s+8)=0

s=20 or s=-8

Garden width: 20-8=12

Garden length: 20-4=16