Right Triangles

Practice Questions

GMAT Quantitative Reasoning › Right Triangles

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1

$\bigtriangleup ABC$ is a right triangle. Evaluate .

Statement 1:

Statement 2:

2

Find the perimeter of right triangle $\Delta XLC$ .

I)

II) $CX=5\sqrt{2}$

3

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What is the length of the height $\overline{AE}$ of right triangle , where $\angle A$ is a right angle?

(1)

(2)

4

What is the height of the right triangle?

The area of the right triangle is .
The base of the right triangle measures .

5

$\bigtriangleup ABC$ is a right triangle. Evaluate .

Statement 1: and

Statement 2: $\bigtriangleup ABC$ has a $60^{\circ }$ angle.

6

$\bigtriangleup ABC$ is a right triangle with right angle $\angle B$ . Evaluate .

Statement 1: and $m \angle A = 30^{\circ }$ .

Statement 2: and $m \angle C = 60^{\circ }$ .

7

$\bigtriangleup ABC$ is a right triangle with right angle $\angle B$ . Evaluate .

Statement 1: $\bigtriangleup ABC$ can be inscribed in a circle with circumference $20 \pi$ .

Statement 2: $\bigtriangleup ABC$ can be inscribed in a cricle with area $100 \pi$ .

8

$\bigtriangleup ABC$ is a right triangle with right angle $\angle B$ . Evaluate .

Statement 1: $\bigtriangleup ABC$ has area 24.

Statement 2: $\bigtriangleup ABC$ can be circumscribed by a circle with area $25 \pi$ .

9

$\bigtriangleup ABC$ is a right triangle. Evaluate .

Statement 1: and

Statement 2: $\bigtriangleup ABC$ is not a 30-60-90 triangle.

10

Altitude

Note: Figure NOT drawn to scale.

Refer to the above diagram.

True or false: $\Delta ABX \cong \Delta ACX$

Statement 1: $\overline{AX}$ is the perpendicular bisector of $\overline{BC}$ .

Statement 2: $\overline{AX}$ is the bisector of $\angle CAB$ .

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