Find the hypotenuse of each isosceles right triangle when the legs are 8

Answer 1

For right triangles, we use the pythagorean theorem: a² + b² = c² . a and b are the legs of the triangle, and c is the hypotenuse. This question asks about an isosceles right triangles, meaning that the legs are the same length. That length is 8.

8² + 8² = c²

64 + 64 = c²

128 = c²

√128 = c² <--- Remember from above, we basically had 64 x 2. Square root of 64 is 8.

8√2 = c

You may also remember that right triangles with equal legs are 45-45-90 triangles, and the hypotenuse is equal to x√2 , which is exactly what we got above.

Answer 2

Use the Pythagorean Theorem a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse. In an isosceles right triangle, the legs are equal. Therefore a and b have the value of 8. We will substitute into the theorem to solve for c, the hypotenuse.. 8^2 + 8^2 = c^2

64 + 64 = c^2 128 = c^2 The square root of 128 equals c. The square root of 128 is 8 times the square root of 2.which is the value of the hypotenuse.