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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 .
An equation is
= .
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:
= ,
= ,
= .
Factor the left size:
= (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.