How to find the height of a 45/45/90 right isosceles triangle - ACT Math
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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?
The area of an isosceles right triangle is
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.
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.
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The area of an isosceles right triangle is 
. What is its height that is correlative and perpendicular to this triangle's hypotenuse?
The area of an isosceles right triangle is
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: 
.
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 are actually looking for is
Therefore, since you know the area, you can say:
Solving, you get:
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What is the area of an isosceles right triangle that has an hypotenuse of length 
?
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 
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:
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
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Find the height of an isoceles right triangle whose hypotenuse is 
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 
where s is side length. Thus, our answer is 
.
To solve simply realize the hypotenuse of one of these triangles is of the form
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