Problem Solving

LUANDATO wrote:

What is the perimeter of the figure above? (Note, figure not necessarilly drawn to scale).

A) 155.
B) 185.
C) 220.
D) 235.
E) 250.

Let's start by adding an auxiliary line that divides the shape into 2 pieces that we can work with (rectangle and right triangle)...


Let x = length of 3rd side of the right triangle...

Since the highlighted triangle is a RIGHT TRIANGLE, we can apply the Pythagorean Theorem.
We get: x² + 40² = 50²
Evaluate to get: x² + 1600 = 2500
So, x² = 900, which means x = 30

Alternatively, we might recognize that the highlighted triangle is a version of the 3-4-5 right triangle, except the highlighted triangle is 10 TIMES bigger than the standard 3-4-5 right triangle, which means the missing side (x) has length 30.....


Now that we have all of the information we need, the perimeter = 30 + 65 + 40 + 65 + 50 = 250
Answer: E