AMC 10 2015a Problem 11

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 $k$? $\textbf{(A)}\ \frac{2}{7} \textbf{(B)}\ \frac{3}{7} \textbf{(C)}\ \frac{12}{25} \textbf{(D)}\ \frac{16}{25} \textbf{(E)}\ \frac{3}{4}$