# ACT Math : How to find the height of a 45/45/90 right isosceles triangle

## Example Questions

### Example Question #1 : 45/45/90 Right Isosceles Triangles

The area of an isosceles right triangle is .  What is its height that is correlative and perpendicular to a side that is not the hypotenuse?

Explanation:

Recall that an isosceles right triangle is a  triangle. That means that it looks like this:

This makes calculating the area very easy! Recall, the area of a triangle is defined as:

However, since  for our triangle, we know:

Now, we know that . Therefore, we can write:

Solving for , we get:

This is the length of the height of the triangle for the side that is not the hypotenuse.

### Example Question #2 : 45/45/90 Right Isosceles Triangles

What is the area of an isosceles right triangle that has an hypotenuse of length ?

Explanation:

Based on the information given, you know that your triangle looks as follows:

This is a  triangle. Recall your standard  triangle:

You can set up the following ratio between these two figures:

Now, the area of the triangle will merely be  (since both the base and the height are ). For your data, this is:

### Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Find the height of an isoceles right triangle whose hypotenuse is

Explanation:

To solve simply realize the hypotenuse of one of these triangles is of the form where s is side length. Thus, our answer is .

### Example Question #4 : 45/45/90 Right Isosceles Triangles

The area of an isosceles right triangle is . What is its height that is correlative and perpendicular to this triangle's hypotenuse?

Explanation:

Recall that an isosceles right triangle is a  triangle. That means that it looks like this:

This makes calculating the area very easy! Recall, the area of a triangle is defined as:

However, since  for our triangle, we know:

Now, we know that . Therefore, we can write:

Solving for , we get:

However, be careful! Notice what the question asks: "What is its height that is correlative and perpendicular to this triangle's hypotenuse?" First, let's find the hypotenuse of the triangle. Recall your standard  triangle: