SOLUTION: Raj and his sister cut the lawn. The lawn is a square and Raj says he will cut a path around the outside 3m wide. His sister will cut the remaining lawn. If the part he cuts is

Question 141577: Raj and his sister cut the lawn. The lawn is a square and Raj says he will cut a path around the outside 3m wide. His sister will cut the remaining lawn. If the part he cuts is the same area as the part she cuts, what are the dimensions of the lawn?
Found 2 solutions by scott8148, edjones:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
"The lawn is a square" __ let x=length (and width)

x^2/2=(x-6)^2 __ x^2=2x^2-24x+72 __ 0=x^2-24x+72

use quadratic formula to find x

Answer by edjones(7569) (Show Source):
You can put this solution on YOUR website!
Let s be the length of the side of the square that the sister will cut.
s^2 The area sister will cut.
(s+6)^2-s^2 The area Raj will cut.
(s+6)^2-s^2=s^2
s^2+12s+36-s^2=s^2
-s^2+12s+36=0
s^2-12s-36=0
s=14.4853 m See below
20.4853 m by 20.4853 m. dimensions of the lawn.
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Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=288 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 14.4852813742386, -2.48528137423857. Here's your graph: