An isosceles right triangle has a hypotenuse of length 22. What is the length of each leg?

Answer 1

To solve this problem, we can use the Pythagorean theorem. We can use this formula because this is a right triangle.

Remember Pythagorean theorem says: a² + b² = c² where c is the length of the hypotenuse and a and b are the legs of the triangle.

An Isosceles right triangle has 2 legs of equal length, so for this triangle a = b.

With this information we can set up a system of equations:

a2+b2= 22

a = b

Plugging the second equation into the first, we get:

b² + b² = 22

2b² = 22

b² = 11

b = √11

Because the second equation states that a = b, we also know that a = √11.

So the length of each leg is √11.