### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #32 : Properties Of Triangles

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:**

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 #33 : Properties Of Triangles

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:**

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 #34 : Properties Of Triangles

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:**

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 #31 : Right Triangles

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

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 #32 : Right Triangles

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

**Possible Answers:**

**Correct answer:**

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 #33 : Right Triangles

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

**Possible Answers:**

**Correct answer:**

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 #38 : Properties Of Triangles

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:**

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.