ACT Math : How to find the length of the side of a 45/45/90 right isosceles triangle
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Example Question #1 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle
A 44/45/90 triangle has a hypotenuse of 
Cannot be determined
It's helpful to remember upon coming across a 45/45/90 triangle that it's a special right triangle. This means that its sides can easily be calculated by using a derived side ratio:
Here, 
Therefore, using the side rules mentioned above, if 
Therefore, the length of one of the legs is 1.
Example Question #2 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle
In a 45-45-90 triangle, if the hypothenuse is 
If the hypotenuse of a 45-45-90 triangle is provided, its side length can only be one length, since the sides of all 45-45-90 triangles exist in a defined ratio of 
Cross-multiply and solve for 
Rationalize the denominator.
You can also solve this problem using the Pythagorean Theorem.
In a 45-45-90 triangle, the side legs will be equal, so 
Substitute the provided length of the hypothenuse and solve for 
While the answer looks a little different from the result of our first method of solving this problem, the two represent the same value, just written in different ways.
Example Question #1 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle
In a 
1. Remember that this is a special right triangle where the ratio of the sides is:
In this case that makes it:
2. Find the perimeter by adding the side lengths together:
Example Question #4 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle
The height of a 
Remember that this is a special right triangle where the ratio of the sides is:
In this case that makes it:
Where 
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