Question

The hypotenuse of a 45°-45°-90° triangle measures 24 inches. What is the length of the one leg of the triangle? 12 in. 12 StartRoot 2 EndRoot in. 24 in. 24 StartRoot 2 EndRoot in.

Answer 1

Answer: 12√2 inches

Step-by-step explanation:

Take a look carefully at the angles of the triangle..first of all it is a right angled triangle & also two of its angles are same (45°)....

Remember the properties of isosceles triangles,if two angles are equal this means opposite sides r also equal..

Let the equal sides be x..

Applying Pythagoras theorem,

x^2 + x^2 = 24^2

Or, 2x^2 = 576

so x^2 = 288

Taking square root on both sides...

x is equal to 12√2 inches