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

## Example Questions

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

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 #193 : Plane Geometry

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 #194 : Plane Geometry

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 #195 : Plane Geometry

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: Since one of your sides is , your hypotenuse is .

Okay, what you are actually looking for is in the following figure: Therefore, since you know the area, you can say: Solving, you get:  