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 
.
