2015 AMC 12A Problem 8

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?

\textbf{(A)}\ \frac27 \qquad\textbf{(B)}\ \frac37 \qquad\textbf{(C)}\ \frac{12}{25} \qquad\textbf{(D)}\ \frac{16}{25} \qquad\textbf{(E)}\ \frac34

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.