2015 AMC 10A Problems/Problem 11

Problem 11

The ratio of the length to the width of a rectangle is  : . If the rectangle has diagonal of length , then the area may be expressed as for some constant . What is ?

$\textbf{(A)}\ \frac{2}{7}\qquad\textbf{(B)}\ \frac{3}{7}\qquad\textbf{(C)}\ \frac{12}{25}\qquad\textbf{(D)}}\ \frac{16}{25}\qquad\textbf{(E)}\ \frac{3}{4}$ (Error compiling LaTeX. Unknown error_msg)

Solution

Let the rectangle have length and width . Then by 3-4-5 triangles (or the Pythagorean Theorem), we have , and so . Hence, the area of the rectangle is , so the answer is