DSQ: Calculating the length of the side of an equilateral triangle

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating the length of the side of an equilateral triangle

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1

Is $\Delta ABC$ an equilateral triangle?

Statement 1: $m\angle A =m\angle B = 60^{\circ }$

Statement 2: $\Delta ABC \sim \Delta DEF$ , and $\Delta DEF$ is equiangular.

2

Given equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , which, if either, is longer, $\overline{AB}$ or $\overline{DE}$ ?

Statement 1:

Statement 2: $BC \cdot EF = 50$

3

Given two equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , which, if either, is greater, or ?

Statement 1:

Statement 2:

4

You are given two equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ .

Which, if either, is greater, or ?

Statement 1: The perimeters of $\bigtriangleup DEF$ and $\bigtriangleup ABC$ are equal.

Statement 2: The areas of $\bigtriangleup DEF$ and $\bigtriangleup ABC$ are equal.

5

What is the length of side $\overline{BC}$ of equilateral triangle $\bigtriangleup ABC$ ?

Statement 1: , , and are all located on a circle with area $576 \pi$ .

Statement 2: The midpoints of all three sides are located on a circle with circumference $24 \pi$ .

6

Find the side length of $\Delta FHT$ .

I) $\Delta FHT$ has perimeter of .

II) $\measuredangle F$ is equal to $\measuredangle T$ which is $60^\circ$ .

7

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ABC is an equilateral triangle inscribed in the circle. What is the length of side AB?

(1) The area of the circle is $16\pi$

(2) The perimeter of triangle ABC is $\frac{36}{\sqrt{3}}$

8

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$\overline{DC}$ is the height of $\bigtriangleup ABC$ . What is the length of $\overline{AB}$ ?

(1) $\overline{DC}=4$

(2) $\overline{DB}=3$

9

What is the length of side $\overline{AB}$ of equilateral triangle $\bigtriangleup ABC$ ?

Statement 1: $\overline{BC}$ is a diagonal of Rectangle with area 30.

Statement 2: $\overline{AC}$ is a diagonal of Square with area 36.

10

$\bigtriangleup ABC$ is equilateral. $\bigtriangleup DEF$ may or may not be equilateral.

which, if either, is longer, $\overline{AB}$ or $\overline{DE}$ ?

Statement 1:

Statement 2: and

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