GMAT Quantitative Reasoning - DSQ: Calculating the perimeter of an equilateral triangle

1

Given three equilateral triangles $\bigtriangleup ABC$ , $\bigtriangleup DEF$ , and $\bigtriangleup GHJ$ , which has the greatest perimeter?

Statement 1: A circle with diameter equal to the length of $\overline{AB}$ can be circumscribed about $\bigtriangleup GHJ$ .

Statement 2: A circle with diameter equal to the length of $\overline{GJ}$ can be circumscribed about $\bigtriangleup DEF$ .

2

Given two equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , which has the greater perimeter?

Statement 1: is the midpoint of $\overline{DE}$ .

Statement 2: is the midpoint of $\overline{DF}$ .

3

Find the perimeter of $\Delta HGY$ given the following:

I) ${}\angle G=\angle H = \frac{\pi}{3}$ .

II) Side .

4

Given an equilateral triangle $\bigtriangleup ABC$ and a right triangle $\bigtriangleup DEF$ with right angle $\angle E$ , which has the greater perimeter?

Statement 1:

Statement 2: $DE = \frac{1}{2} \cdot AB$

5

Given three equilateral triangles $\bigtriangleup ABC$ , $\bigtriangleup DEF$ , and $\bigtriangleup GHJ$ , which has the greatest perimeter?

Statement 1:

Statement 2:

6

Given two equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , which, if either, has the greater perimeter?

Statement 1:

Statement 2: $\bigtriangleup ABC$ has greater area than $\bigtriangleup DEF$ .

7

Given two equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , which, if either, has the greater perimeter?

Statement 1: $\frac{AC}{DE} = \frac{5}{6}$

Statement 2:

8

Which, if either, is greater: the perimeter of equilateral triangle $\bigtriangleup ABC$ or the circumference of a given circle with center ?

Statement 1: The midpoint of $\overline{AC}$ is inside the circle.

Statement 2: The midpoint of $\overline{AB}$ is on the circle.

9

Which, if either, of equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , has the greater perimeter?

Statement 1: $2 \cdot AB + 3 \cdot DE =44$

Statement 2: $3 \cdot BC+ 4 \cdot DF= 62$

10

Give the perimeter of equilateral triangle $\bigtriangleup ABC$ .

Statement 1: $\overline{AB}$ is a radius of a circle with area $64 \pi$ .

Statement 2: $\overline{BC}$ is the hypotenuse of a 30-60-90 triangle with area $8 \sqrt{3}$ .

DSQ: Calculating the perimeter of an equilateral triangle

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