The two legs of a right triangle are equal and the square of its hypotenuse is 50. Find the length of each leg.

To find the length of each leg in a right triangle where the legs are equal and the square of the hypotenuse is 50, we can use the Pythagorean theorem. This theorem states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.

Setting Up the Equation

Let the length of each leg be represented by x. According to the Pythagorean theorem, we have:

• x² + x² = hypotenuse²

Since the hypotenuse squared is given as 50, we can rewrite the equation:

• 2x² = 50

Solving for x

Now, let's solve for x:

• Divide both sides by 2: x² = 25
• Take the square root of both sides: x = 5

Final Answer

Therefore, the length of each leg of the triangle is 5 units.