What is the perimeter of the figure above?

[Gmat_mission]

What is the perimeter of the figure above?

(A) 380

(B) 360

(C) 330

(D) 300

(E) 230

[spoiler]OA=A[/spoiler]

Source: Official Guide

[Brent@GMATPrepNow]

kCko6To.jpg

What is the perimeter of the figure above?

(A) 380

(B) 360

(C) 330

(D) 300

(E) 230

[spoiler]OA=A[/spoiler]

Source: Official Guide

Draw a perpendicular line as follows:


From here, we have two different ways to find the value of x

Approach #1: Recognize that 60 and 100 are each 20 times the lengths of the basic 3-4-5 right triangle.
That is (20)(3) = 60 and (20)(5) = 100
So, x = (20)(4) = 80

Approach #2: Apply the Pythagorean theorem
We get: 60² + x² = 100²
Simplify: 3,600 + x² = 10,000
Subtract 3,600 from both sides to get: x² = 6,400
Solve: x = 80

At this point we can find the perimeter....

Perimeter = 60 + 70 + 100 + 80 + 70 = 380

Answer: A

Cheers,
Brent

[Scott@TargetTestPrep]

kCko6To.jpg

What is the perimeter of the figure above?

(A) 380

(B) 360

(C) 330

(D) 300

(E) 230

[spoiler]OA=A[/spoiler]

Source: Official Guide

Solution:

In order to determine the perimeter of the figure, we need to determine the length of the base of the figure. We can drop a pendicular from the vertex where the 70 and the 100 sides meet to the base of the figure. We see that the figure is divided into a rectangle on the left and a right triangle on the right. The base of the right triangle must be 80 since the height (i.e., the perpendicular dropped) is 60 and the hypotenuse is 100 (so the triangle is actually a 3-4-5 right triangle, with each dimension multiplied by 20, creating a 60-80-100 right triangle). Therefore, the entire base of the figure is 70 + 80 = 150, and the perimeter of the figure is 60 + 70 + 100 + 150 = 380.

Answer: A