Equilateral Triangles

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GMAT Quantitative › Equilateral Triangles

Questions 1 - 10
1

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

Not enough information to solve

Explanation

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

. Plugging in the values provided:

2

A given equilateral triangle has a side length and a height . What is the area of the triangle?

Not enough information provided

Explanation

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

. Plugging in the values provided:

3

If an equilateral triangle has a side length of and a height of , what is the area of the given triangle?

Explanation

To find the area of a traingle, we need the height and base lengths. Plug the given values into the following formula:

4

Find the perimeter of an equilateral triangle whose side length is .

Explanation

To find the perimeter, you must multiply the side length by . Thus,

5

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

Not enough information to solve

Explanation

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

. Plugging in the values provided:

6

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

Explanation

We derive the equation of base of a triangle from the area of a triangle formula:

7

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

Explanation

The area of an equilateral triangle with sidelength is

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

8

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Equilateral triangle is inscribed in a circle with radius , what is the length of a side of the triangle?

Explanation

Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located away from the edge of a given height.

Therefore 5, the radius of the circle is of the height.

Therefore, the height must be .

From here, we can use the formula for the height of the equilateral triangle , where is the length of the height and is the length of a side of the equilateral triangle.

Therefore, , then is the final answer.

9

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is an equilateral triangle inscribed in a cirlce with radius . What is the area of the triangle ?

Explanation

Since we are given a radius for the circle, we should be able to find the length of the height of the equilateral triangle, indeed, the center of the circle is of the length of the height from any vertex.

Therefore, the height is where is the length of the height of the triangle. Therefore .

We can now plug in this value in the formula of the height of an equilateral triangle, where is the length of the side of the triangle.

Therefore, or .

Now we should plug in this value into the formula for the area of an equilateral triangle where is the value of the area of the equilateral triangle. Therefore , which is our final answer.

10

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

Explanation

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 .

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