Tom K. answered • 09/15/21

Knowledgeable and Friendly Math and Statistics Tutor

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

400 - 82x + 4x^{2} = 162

4x^{2} - 82x + 238 = 0

2(2x^{2} - 41x + 119) = 0

2x^{2} - 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.