SOLUTION: The diagonal of a rectangle measures 10 inches. If the length is 2 inches more than the width, find the dimensions of the rectangle.

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Question 1010064: The diagonal of a rectangle measures 10 inches. If the length is 2 inches more than the width, find the dimensions of the rectangle.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The diagonal of a rectangle measures 10 inches. If the length is 2 inches more than the width, find the dimensions of the rectangle.
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Let x be the length of the rectangle, in inches.

Then the width is x-2 inches, and the diagonal is sqrt%28x%5E2+%2B+%28x-2%29%5E2%29.

An equation is

sqrt%28x%5E2+%2B+%28x-2%29%5E2%29 = 10.

The (3,4,5) triangle came into the mind with the legs of 6 inches and 8 inches, but I will complete the solution algebraically.

Square both sides of the equation (1), then simplify step by step:

x%5E2+%2B+%28x-2%29%5E2 = 100,

2x%5E2+-+2x+%2B+4+-+100 = 0,

x%5E2+-+x+-+48 = 0.


Factor the left size:

x%5E2+-+x+-+48 = (x+6)*(x-8) = 0.

Now it is clear that x = 8 inches is the solution of the problem.

The rectangle has the dimensions 8 inches and 6 inches.