# SSAT Upper Level Math : How to find the height of a right triangle

## Example Questions

### Example Question #1 : How To Find The Height Of A Right Triangle

If the hypotenuse of a right triangle is 20, and one of the legs is 12, what is the value of the other leg?

Explanation:

The triangle in this problem is a variation of the 3, 4, 5 right triangle. However, it is 4 times bigger. We know this because  (the length of the hypotenuse) and  (the length of one of the legs).

Therefore, the length of the other leg will be equal to:

### Example Question #2 : How To Find The Height Of A Right Triangle

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

Not enough information provided

Explanation:

For a given right triangle with base  and height , the area  can be defined by the formula . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area  as follows:

Plugging in our values for  and :

### Example Question #3 : How To Find The Height Of A Right Triangle

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

Not enough information provided

Explanation:

For a given right triangle with base  and height , the area  can be defined by the formula . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area  as follows:

Plugging in our values for  and :

### Example Question #4 : How To Find The Height Of A Right Triangle

A given right triangle has a hypotenuse of  and a total area of . What is the height of the triangle?

Not enough information provided

Not enough information provided

Explanation:

For a given right triangle with base  and height , the area  can be defined by the formula . If one leg of the right triangle is taken as the base, then the other leg is the height.

However, we have not been given a base or leg length for the right triangle, only the length of the hypotenuse and the area. We therefore do not have enough information to solve for the height

### Example Question #5 : How To Find The Height Of A Right Triangle

The area of a right triangle is . If the base of the triangle is , what is the height, in meters?

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

Use the information given in the question:

Now, solve for the height.

### Example Question #6 : How To Find The Height Of A Right Triangle

The area of a right triangle is , and the base is . What is the height, in meters?

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

Use the information given in the question:

Now, solve for the height.

### Example Question #7 : How To Find The Height Of A Right Triangle

The area of a right triangle is . If the base of the triangle is , what is the length of the height, in inches?

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

Use the information given in the question:

Now, solve for the height.