Each leg of a 45°-45°-90° triangle measures 12 cm. triangle x y z is shown. angle x y z is a right angle and angles y z x and z x y are 45 degrees. the lengths of sides z y and y x are 12 centimeters. what is the length of the hypotenuse? 6 cm 6 startroot 2 endroot cm 12 cm 12 startroot 2 endroot cm

The length of the hypotenuse is cm and this can be determined by using the Pythagorean theorem.

Given :

The length of the hypotenuse can be determined by using the Pythagorean theorem. According to this theorem, the square of the longer side is equal to the sum of the square of the shorter sides.

 ---- (1)

where H is the hypotenuse, B is the base and P is the perpendicular.

Now, put the value of P and B in equation (1).

For more information, refer to the link given below:

link

Step-by-step explanation:

Pythagorean theorem: In a right triangle with legs a, b and hypotenuse c,

Given: ΔXYZ is right triangle with right angle Y.

Angles YZX and ZXY are 45 degrees.

ZY = YX = 12 cm

Find: XZ

Solution:

By the Pythagorean theorem,

answer is 144

step-by-step explanation: