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

Study concepts, example questions & explanations for SSAT Upper Level Math

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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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Not enough information provided

Correct answer:

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?

Possible Answers:

Not enough information provided

Correct answer:

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?

Possible Answers:

Not enough information provided

Correct answer:

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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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.

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