The two legs of a right triangle are equal and the square of its hypotenuse is 50 .find the length of each leg
Both sides of the triangle are equal, and the hypotenuse is 50, then
Let "x" represent the sides of the triangle.
x^2 + x^2 = 50
2x^2 = 50
2x^2 / 2 = 50 / 2
x^2 = 25
sqrt(x) = sqrt(25)
x = 5
To find the length of each leg of a right triangle, we need to solve for the unknown sides using the given information.
Let's assume the length of each leg is "x". According to the given information, the two legs of the triangle are equal, so both legs have a length of "x".
We can now use the Pythagorean theorem to solve for the length of the hypotenuse. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have:
x^2 + x^2 = 50
Combining like terms:
2x^2 = 50
Dividing both sides of the equation by 2:
x^2 = 25
Taking the square root of both sides:
x = √25
x = 5
Therefore, each leg of the right triangle has a length of 5.