Solving Quadratics

Question

A rectangular lawn measures 30 m by 40 m. Jason is cutting the lawn from the outside perimeter in toward the centre by cutting strips along the entire perimeter first, then continuing as he cuts toward the centre. How wide is the strip that has been cut along the outside when the area is half cut?

I'm confused on how to make the equation to solve for x. I know that the one side of the equation is equal to 600, but i'm not sure about the other side of the equation.

score 1 · Accepted Answer · answered Sep 15 '13 at 17:21

1

Hint: Draw a picture. Let $x$ be the width of the strip. So $2x$ has been removed from both length and width of the lawn.

Then what is left is a $(30-2x)\times (40-2x)$ rectangle. This has area $600$. Now you can solve for $x$.

answered Sep 15 '13 at 17:21

André Nicolas

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And if you then notice that $(30-2x)(40-2x)=(35-2x)^2-25$ it becomes even easier. – Mark Bennet Sep 15 '13 at 17:49
@Mark Bennet: Nice observation, completing the square can be done without expanding. – André Nicolas Sep 15 '13 at 17:52

Solving Quadratics

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