1952 AHSME Problems/Problem 39
Problem
If the perimeter of a rectangle is and its diagonal is , the difference between the length and width of the rectangle is:
Solution
Let the sides of the rectangle be x and y. WLOG, assume x>y. Then, .
By pythagorean theorem, .
Since , .
Rearranging to solve for gives .
Rearranging in terms of the defined variables becomes .
In order to get (x-y), we have to take the square root of the expression and simplify.
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See also
1952 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 38 |
Followed by Problem 40 | |
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