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Area of Rectangle as a Function of Diagonal's Length

Source: 2015 AMC 12A #8/10A #11

February 4, 2015
geometryrectanglefunctionratioPythagorean TheoremAMC

Problem Statement

The ratio of the length to the width of a rectangle is 4:34:3. If the rectangle has diagonal of length dd, then the area may be expressed as kd2kd^2 for some constant kk. What is kk?
<spanclass=′latex−bold′>(A)</span>27<spanclass=′latex−bold′>(B)</span>37<spanclass=′latex−bold′>(C)</span>1225<spanclass=′latex−bold′>(D)</span>1625<spanclass=′latex−bold′>(E)</span>34<span class='latex-bold'>(A) </span>\dfrac27\qquad<span class='latex-bold'>(B) </span>\dfrac37\qquad<span class='latex-bold'>(C) </span>\dfrac{12}{25}\qquad<span class='latex-bold'>(D) </span>\dfrac{16}{25}\qquad<span class='latex-bold'>(E) </span>\dfrac34
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