Question

The chicken coop at the petting farm is 10 x 14‘. The farm would like to double the current area by adding the same amount, X, to the length and width. What are the dimensions of the new enclosure? Round to the nearest hundredth of a foot

Answer 1

x = 4.85 feet

Explanation:

Original area of the petting farm = 10 × 14

= 140 square feet

.

New area = double the original area = 140 * 2

= 280 square feet

New area of the petting farm =

Width × length

280 = (10+x) × (14+x)

280 = 140 + 10x + 14x + x²

280 - 140 = x² + 24x

140 = x² + 24x

x² + 24x - 140 = 0

Solve the quadratic equation

x = -b ± √b² - 4ac / 2a

= -24 ± √(24)² - 4*1*-140 / 2*1

= -24 ± √ 576 - (-560) / 2

= -24 ± √ 576 + 560 / 2

= -24 ± √1,136 / 2

= -24 ± 4√71 / 2

= -24/2 ± 4√71/2

= -12 ± 2√71

x = 4.8523 or x = -28.8583

x can not be a negative value

Therefore,

x = 4.85 feet to the nearest hundredth