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

1

Given equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , construct the altitude from to on $\overline{BC}$ , and the altitude from to on $\overline{EF}$ .

Which, if either, is longer, $\overline{AM}$ or $\overline{DN}$ ?

Statement 1:

Statement 2: $\frac{DM}{BM} = \frac{3}{2}$

2

$\bigtriangleup ABC$ is an equilateral triangle. An altitude of $\bigtriangleup ABC$ is constructed from to a point on $\overline{BC}$ .

What is the length of $\overline{AM}$ ?

Statement 1: $\bigtriangleup ABC$ has perimeter 36.

Statement 2: $\bigtriangleup ABC$ has area $36\sqrt{3}$ .

3

$\bigtriangleup ABC$ is an equilateral triangle. An altitude of $\bigtriangleup ABC$ is constructed from to a point on $\overline{AB}$ .

What is the length of $\overline{CM}$ ?

Statement 1: $\bigtriangleup ABC$ is inscribed inside a circle of circumference $24 \pi$ .

Statement 2: $\overline{BC}$ is a chord of a circle of area $108 \pi$ .

4

Given equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , construct the altitude from to on $\overline{BC}$ , and the altitude from to on $\overline{EF}$ .

True or false: $\overline{AM}$ or $\overline{DN}$ have the same length.

Statement 1: $\overline{AM}$ and $\overline{DN}$ are chords of the same circle.

Statement 2: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ have the same area.

5

$\bigtriangleup ABC$ is an equilateral triangle. An altitude of $\bigtriangleup ABC$ is constructed from to a point on $\overline{AB}$ .

True or false:

Statement 1: A circle of area less than $16 \pi$ can be inscribed inside $\bigtriangleup ABC$ .

Statement 2: $\overline{BC}$ is a chord of a circle of area $27 \pi$ .

6

Given equilateral triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , construct the altitude from to on $\overline{BC}$ , and the altitude from to on $\overline{EF}$ .

Which, if either, of $\overline{AM}$ and $\overline{DN}$ is longer?

Statement 1:

Statement 2:

7

Given $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with $\bigtriangleup ABC$ an equilateral triangle. Construct the altitude from to on $\overline{BC}$ , and the altitude from to on $\overleftrightarrow{EF}$ .