Question

The figure above shows a path around a triangular piece of land. Mary walked the distance of $8$ miles from P to Q and then walked the distance of $6$ miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

• A. $30\%$
• B. $40\%$
• C. $50\%$
• D. $60\%$
• E. $80\%$

Answer 1

Answer: (B)

Mary walked a total distance of $8+6$ $=$ $14$ miles

In right triangle PQR, (PR) ${}^2$ $=$ (PQ)${}^2$ + (QR)${}^2$

So, PR $=$ 10 miles

Ted walked directly from P to R (10 miles)

So, Mary walked $14-10$ $=$ $4$ miles extra.

So, percentage wise,

$\frac{4}{10}\times 100$ $=$ $40\%$ (option B)