Question

10.) Your dad is planning to increase the area of your rectangular patio. Your current patio is 8

feet by 10 feet, and your dad plans to double its area by adding the same amount x to its length
and width. Find the value of x, and the new dimensions of the patio.

Answer 1

x = 3.69 feet

11.69 x 13.69 feet

new area = (8 x 10) x 2 = 160

(8 + x)(10 + x) = 160

80 + 8x + 10x + x² = 160

combine like terms:

x² + 18x - 80 = 0

factor:

(x - 3.69)(x + 21.69) = 0

x = 3.69

Answer 2

x = 3.69 feet

11.69 x 13.69 feet

Explanation:

new area = (8 x 10) x 2 = 160

(8 + x)(10 + x) = 160

80 + 8x + 10x + x² = 160

combine like terms:

x² + 18x - 80 = 0

factor:

(x - 3.69)(x + 21.69) = 0

x = 3.69