SOLUTION: A square lawn is bounded on 3 sides by a path 4 meter wide. If the area of the path is 7/8 that of the lawn, find the dimensions of the lawn.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A square lawn is bounded on 3 sides by a path 4 meter wide. If the area of the path is 7/8 that of the lawn, find the dimensions of the lawn.      Log On


   

Question 762202: A square lawn is bounded on 3 sides by a path 4 meter wide. If the area of the path is 7/8 that of the lawn, find the dimensions of the lawn.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A drawing really helps with this problem.
Using s = the side length of the square lawn,
Area of just the lawn = s%5E2
Area of path plus lawn = %28s%2B4%29%28s%2B2%2A4%29
Area of ONLY the path = %28s%2B4%29%28s%2B2%2A4%29-s%5E2

AND using the 7/8 information, highlight%28%28s%2B4%29%28s%2B2%2A4%29-s%5E2=%287%2F8%29s%5E2%29
Solve for s, of course after first simplifying...
.
.
7s%5E2-96x-256=0
s=%2896%2Bsqrt%2896%5E2%2B4%2A7%2A256%29%29%2F14
s=%2896%2B2%5E6%29%2F14
highlight%28s=80%2F7%29
or
11%263%2F7