How to find the height of an acute / obtuse triangle

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SSAT Upper Level Quantitative › How to find the height of an acute / obtuse triangle

Questions 1 - 10

1

The area of a triangle is , and the base of the triangle is . What is the height for this triangle?

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$240=\frac{30 \times h}{2}$

The height of the triangle is .

2

A triangle has an area of and a base of . In meters, find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$360=\frac{60\times h}{2}$

The height of the triangle is meters.

3

A triangle has an area of and a base of . Find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$45=\frac{15\times h}{2}$

The height of the triangle is .

4

A triangle has an area of and a base of . Find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$24=\frac{12\times h}{2}$

The height of the triangle is .

5

A triangle has an area of and a base of . Find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$54=\frac{12\times h}{2}$

The height of the triangle is .

6

A triangle has an area of and a base of . Find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$60=\frac{12\times h}{2}$

The height of the triangle is .

7

A triangle has an area of and a base of . In terms of , find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$24x^2=\frac{6x\times h}{2}$

$h=\frac{48x^2}{6x}=8x$

The height of the triangle is .

8

A triangle has an area of and a base of . In terms of , find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$128y^2=\frac{16y\times h}{2}$

The height of the triangle is .

9

A triangle has an area of and a base of . What is the height?

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$48a=\frac{6a\times h}{2}$

$h=\frac{96a}{6a}=\frac{96}{6}=16$

The height of the triangle is .

10

A triangle has an area of and a base of . Find the height.

Explanation

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$56t=\frac{7t\times h}{2}$

$h=\frac{112t}{7t}=\frac{112}{7}=16$

The height of the triangle is .

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