DSQ: Calculating the length of the side of a right triangle

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating the length of the side of a right triangle

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1

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

Statement 1: and

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

2

$\bigtriangleup ABC$ 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 $25 \pi$ .

3

$\bigtriangleup ABC$ 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 $100 \pi$ .

4

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

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

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

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. Evaluate .

Statement 1:

Statement 2:

7

Given $\bigtriangleup ABC$ is a right triangle, which side is the hypotenuse - $\overline{AB}$ , $\overline{AC}$ , or $\overline{BC}$ ?

Statement 1:

Statement 2:

8

Given $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , which, if either, is the longer of the two: $\overline{AC}$ or $\overline{DF}$ ?

Statement 1:

Statement 2: $\angle B$ is a right angle and $\angle E$ is an obtuse angle

9

$\bigtriangleup ABC$ has right angle $\angle B$ ; $\bigtriangleup DEF$ has right angle $\angle E$ . Which, if either, is longer, $\overline{AC}$ or $\overline{DF}$ ?

Statement 1:

Statement 2: $\angle A \cong \angle C \cong \angle D \cong \angle F$

10

$\bigtriangleup ABC$ has right angle $\angle B$ ; $\bigtriangleup DEF$ has right angle $\angle E$ . Which, if either, is longer, $\overline{AC}$ or $\overline{DF}$ ?

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

Statement 2: $m \angle D = 45^{\circ }$

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