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Question

The ratio of the length to the width of a rectangle is 4 : 3. If the rectangle has diagonal of length d, then the area may be expressed as kd^2 for some constant k. What is k?

Accepted Answer

Let the rectangle have length 4x and width 3x. Then by 3-4-5 triangles (or the Pythagorean Theorem), we have d = 5x, and so x = d5. Hence, the area of the rectangle is 3x 4x = 12x^2 = 12d^225, so the answer is 1225