How do you find the third side of a right triangle if the base is x = 20m, and height is y = 20m?

1 Answer
Meave60
Jun 6, 2015

The third side is the hypotenuse, which is 20sqrt 2"m".

This is an example of an iscoseles right triangle, in which the angles are 45-45-90 degrees. In an iscoseles right triangle, the base and height are the same. The hypotenuse is the missing side and is equal to "L"sqrt2, where "L" refers to either of the other two legs, which are equal. Therefore, the length of the hypotenuse is 20sqrt 2"m".

We can use the Pythagorean theorem to prove this: c^2=a^2+b^2. Let side x=a=20"m" and side y=b=20"m". The hypotenuse is c.

c^2=(20"m")^2+(20"m")^2 =

c^2=400"m"^2+400"m"^2

c^2=800"m"^2"

c=sqrt(800"m"^2) =

c=sqrt(20xx20xx2xx"m"^2) =

c=20sqrt2"m"

![http://www.platinumgmat.com/gmat_study_guide/pythagorean_theorem](useruploads.socratic.org)

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