Question

A rectangular flower garden, 7 m by 6 m, is surrounded by a grass strip of uniform width. If the total area of the garden and the grass strip is 90 m^2, what is the width of the strip?

To solve this, I used the formula 90=(6+2x)(7+2x) where is is the width of one ised, but since it's surrounded on all sides, I used 2x. The problem is, I'm getting a negative answer; the back of the books tells me I should be getting 1.5m as an answer, but I'm clearly doing something wrong. I just don't know what though and would really appreciate help understanding my errors.

Answer 1

4 x^2 + 26 x + 42 = 90
4 x^2 + 26 x - 48 = 0
2 x^2 + 13 x - 24 = 0
(2 x - 3)( x + 8) = 0
2x = 3 or x = -8
x = 3/2 or x = -8
use x = 3/2 = 1.5