### All GMAT Math Resources

## Example Questions

### Example Question #7 : Calculating The Area Of An Equilateral Triangle

A given right triangle has a base of length and a height . What is the area of the triangle?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

For a given right triangle with a side length and a height , the area is

. Plugging in the values provided:

### Example Question #11 : Equilateral Triangles

If the area of an equilateral is , given a base of , what is the height of the triangle?

**Possible Answers:**

**Correct answer:**

We derive the height formula from the area of the triangle formula:

### Example Question #12 : Equilateral Triangles

What is the height of an equilateral triangle with sidelength 20?

**Possible Answers:**

**Correct answer:**

The area of an equilateral triangle with sidelength is

Using this area for and 20 for in the general triangle formula, we can obtain :

### Example Question #13 : Equilateral Triangles

An equilateral triangle has a side length of . What is the height of the triangle?

**Possible Answers:**

**Correct answer:**

The height of an upright equilateral triangle is the perpendicular distance from the center of its base to its top. We can imagine that this line cuts the equilateral triangle into two congruent right triangles whose height is half the length of the original base and whose hypotenuse is the original side length. In these two congruent triangles, their base, which is the height of the equilateral triangle, is the only unknown side length, so we can use the Pythagorean theorem to solve for it:

### Example Question #14 : Equilateral Triangles

is an equilateral triangle, with a side length of . What is the height of the triangle?

**Possible Answers:**

**Correct answer:**

We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:

, where is the length of a side and the length of the height.

Therefore, the final answer is .

### Example Question #15 : Equilateral Triangles

Given that an equilateral triangle has side lengths equal to , determine it's height in simplest form.

**Possible Answers:**

**Correct answer:**

To solve, we must use pythagorean's theorem given that we know the hypotenuse is and one side length is . Therefore:

### Example Question #16 : Equilateral Triangles

The area of an equilateral triangle is . What is the perimeter of ?

**Possible Answers:**

**Correct answer:**

The area is given, which will allow us to calculate the side of the triangle and hence we can also find the perimeter.

The area for an equilateral triangle is given by the formula

, where is the length of the side of the triangle.

Therefore, , where is the area.

Thus , and the perimeter of an equilateral triangle is three times the side, hence, the final answer is .

### Example Question #17 : Equilateral Triangles

A given equilateral triangle has a side length of . What is the perimeter of the triangle?

**Possible Answers:**

Not enough information provided.

**Correct answer:**

An equilateral triangle with a side length has a perimeter .

Given:

,

.

### Example Question #18 : Equilateral Triangles

A given equilateral triangle has a side length of . What is the perimeter of the triangle?

**Possible Answers:**

**Correct answer:**

An equilateral triangle with a side length has a perimeter .

Given:

,

.

### Example Question #19 : Equilateral Triangles

A given equilateral triangle has a side length of . What is the perimeter of the triangle?

**Possible Answers:**

Not enough information provided.

**Correct answer:**

An equilateral triangle with a side length has a perimeter .

Given:

,

.