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 k d^{2} for some constant k. What is k ?

**Answer Choices**

A. \dfrac{2}{7}

B. \dfrac{3}{7}

C. \dfrac{12}{25}

D. \dfrac{16}{25}

E. \dfrac{3}{4}