ACT Math : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem
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Example Question #5 : Triangles
Square 
Cannot be determined from the information provided
The answer can be found two different ways. The first step is to realize that this is really a triangle question, even though it starts with a square. By drawing the square out and adding the diagonal, you can see that you form two right triangles. Furthermore, the diagonal bisects two ninety-degree angles, thereby making the resulting triangles a 
From here you can go one of two ways: using the Pythagorean Theorem to find the diagonal, or recognizing the triangle as a 
1) Using the Pythagorean Theorem
Once you recognize the right triangle in this question, you can begin to use the Pythagorean Theorem. Remember the formula: 
In this case, 
The length of the diagonal is 
2) Using Properties of 
The second approach relies on recognizing a 
In this case, 
Therefore, using the 
Example Question #2 : Triangles
What is the length of the hypotenuse of an isosceles right triangle with an area of 
Recall that an isosceles right triangle is also a 
Therefore, the area of the triangle is:
For our data, this means:
Solving for 
So, your triangle looks like this:
Now, you can solve this with a ratio and easily find that it is 
Now, just do your math carefully:
That is a weird kind of factoring, but it makes sense if you distribute back into the group. This means you can simplify:
Example Question #6 : Triangles
When the sun shines on a 
The pole and its shadow make a right angle. Because they are the same length, they form an isosceles right triangle (45/45/90). We can use the Pythagorean Theorem to find the hypotenuse. 
Example Question #151 : Triangles
Find the hypotenuse of an isosceles right triangle given side length of 3.
To solve, simply use the Pythagorean Theorem.
Recall that an isosceles right triangle has two leg lengths that are equal.
Therefore, to solve for the hypotenuse let 
Thus,
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