ACT Math : How to find the height of a 45/45/90 right isosceles triangle
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Example Question #1 :45/45/90 Right Isosceles Triangles
The area of an isosceles right triangle is
Recall that an isosceles right triangle is a
This makes calculating the area very easy! Recall, the area of a triangle is defined as:
However, since
Now, we know that
Solving for
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
Based on the information given, you know that your triangle looks as follows:
This is a
You can set up the following ratio between these two figures:
Now, the area of the triangle will merely be
Example Question #3 :45/45/90 Right Isosceles Triangles
Find the height of an isoceles right triangle whose hypotenuse is
To solve simply realize the hypotenuse of one of these triangles is of the form
Example Question #4 :45/45/90 Right Isosceles Triangles
The area of an isosceles right triangle is
Recall that an isosceles right triangle is a
This makes calculating the area very easy! Recall, the area of a triangle is defined as:
However, since
Now, we know that
Solving for
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
Since one of your sides is
Okay, what you areactuallylooking for is
Therefore, since you know the area, you can say:
Solving, you get:
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