The two legs of a right triangle are equal and the square of its hypotenuse is 50 .find the length of each leg
x^2 + x^2 = 50
x^2 = 25
x = 5
To find the length of each leg of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
Let's assume the length of each leg is "x". According to the given information, the square of the hypotenuse is 50, so we have:
x^2 + x^2 = 50
Simplifying this equation:
2x^2 = 50
Dividing both sides by 2:
x^2 = 25
To solve for "x", we take the square root of both sides:
√(x^2) = √25
x = ±√25
Since the length of a side cannot be negative, we take the positive square root:
x = √25
x = 5
Therefore, each leg of the right triangle has a length of 5 units.