McGraw-Hill Education GRE 2019

12

4

A

BC

D

3

What is the perimeter of the figure above?

SOLUTION: To determine the perimeter, you need to add up all the sides.

You know all the side-lengths except CD. To solve for CD, first solve for AC.

The legs of right triangle ABC have lengths of 3 and 4, so AC = 5. If AC = 5

and AD = 12, then CD = 13. The perimeter of the figure is thus 3 + 4 + 12 +

13 = 32.

However, be careful about assuming that any right triangle with two side

lengths from the Pythagorean triplets will necessarily conform to the preceding

list. The triplets only apply in situations where the largest value of the triplet is the

length of the hypotenuse:

B

3 4

A C

QUANTITY A QUANTITY B

length of AC 5

SOLUTION: Even though ABC is a right triangle with two sides of 3 and 4, it is

not a Pythagorean triplet. The side with length 4 is the hypotenuse, which

means that the length of AC must be less than 4. Thus Quantity B is greater.

Isosceles Right Triangles and the Diagonal of a Square

In addition to the Pythagorean triplets, there are two other triangle combinations

that you will need to know for the GRE: isosceles right triangles and 30-60-90

triangles.

An isosceles right triangle is any right triangle in which the lengths of the legs

are equal. Since the lengths of the legs are equal, their corresponding angles will

also be equal, with each having a measurement of 45 degrees. Thus another term

for an isosceles right triangle is a 45-45-90 triangle.

382 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 382 23/01/18 11:10 AM