Quadratic equation help

Question

Jim is landscaping his backyard which is 16‘ x 25‘. He will buy 162 ft.² of sod to put in the middle leaving a uniform with around the four edges for planting flowers. What dimensions will the sod have?

Answer 1

Draw a picture. (16 - 2x)(25 - 2x) = 162

400 - 82x + 4x² = 162

4x² - 82x + 238 = 0

2(2x² - 41x + 119) = 0

2x² - 41x + 119 = 0

(2x - 7)(x - 17) = 0

x = 17, 7/2

Note that 17 is invalid, because then the two dimensions 16 - 2x and 25 - 2x will be negative

As a check of 7/2, (16 - 2(7/2))(25 - 2(7/2)) = 9(18) = 162

The dimensions, of course, of the sod are 18 x 9.