How to find the height of a 45/45/90 right isosceles triangle
Help Questions
ACT Math › 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
.
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.
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: .
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: