Question

The hypotenuse of a 45°-45°-90° triangle measures 22 StartRoot 2 EndRoot units.

A right triangle is shown. The length of the hypotenuse is 22 StartRoot 2 EndRoot 2 units. The lengths of the other 2 sides are congruent.

What is the length of one leg of the triangle?

Answer 1

The length of one leg of the 45°-45°-90° triangle, when the hypotenuse is 22√2 units, is 22 units.

Step-by-step explanation:

The question being asked is about finding the length of one leg of a 45°-45°-90° triangle when the hypotenuse is known. In a 45°-45°-90° triangle, the legs have equal lengths, and the length of the hypotenuse (√c) is √2 times the length of one leg (a), according to the properties of special right triangles. This can be expressed as c = a√2. If we are given that the hypotenuse of the triangle is 22√2 units, we can find the length of one leg by diving the hypotenuse by √2. Therefore, the calculation would be 22√2 ÷ √2 = 22 units, which is the length of one leg.