SOLUTION: The length of a rectangle is 7 feet more than its width. The diagonal of the rectangle is 13 feet. Find the dimensions of the rectangle.

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Question 1131888: The length of a rectangle is 7 feet more than its width. The diagonal of the rectangle is 13 feet. Find the dimensions of the rectangle.
Found 2 solutions by ikleyn, joshuajz:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the Pythagorean theorem to get an equation


w^2 + (W+7)^2 = 13^2.


Then solve this equation to find the width of the rectangle.


Answer by joshuajz(12) About Me  (Show Source):
You can put this solution on YOUR website!
The first thing I'd do is create a drawing.

Next you need to know the equation of the diagonal of a shape (The Pythagorean theorem):
d%5E2+=+w%5E2+%2B+h%5E2
Meaning we can now write an equation to solve for x
%28x%5E2+%2B+%28x%2B7%29%5E2%29+=+13%5E2
%28x%5E2+%2B+x%5E2+%2B+14x+%2B+49%29+=+169
2x%5E2+%2B+14x+-+120+=+0
Since this is in standard form and equal to 0 we can use the quadratic formula: %28-b%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
%28-14%2B-+sqrt%2814%5E2-4%2A2%2A-120%29%29%2F%282%2A2%29
Therefore:
x+=+-+12 OR x+=+5
Since a side length cannot be negative, we can "Throw away" the x+=+-12
Therefore: x = 5
Meaning the dimensions of the rectangle are 5 x 12