the two legs of a right 6triangle are equal and the square of its hypotenuse is 50.find the length of each legs
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 square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Given that the square of the hypotenuse is 50, we can set up the equation:
Let x be the length of each leg.
x^2 + x^2 = 50
Simplifying the equation:
2x^2 = 50
Divide both sides of the equation by 2:
x^2 = 25
Taking the square root of both sides:
x = √25
Since we are interested in the length, we take the positive square root:
x = 5
Therefore, each leg of the right triangle has a length of 5 units.