What is the value of x in the triangle?
an isosceles right triangle with two legs of length 10 and hypotenuse of length x
In an isosceles right triangle, the two legs are congruent (equal in length) because the angles opposite to them are congruent.
Let's label the legs as a and the hypotenuse as c. In this case, both legs have a length of 10, so a = 10.
Using the Pythagorean theorem, we can find the value of c (the hypotenuse) when we know the lengths of the legs. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
c^2 = a^2 + a^2
c^2 = 10^2 + 10^2
c^2 = 100 + 100
c^2 = 200
Taking the square root of both sides:
c = √200
The value of the hypotenuse (x) is approximately 14.142.
Therefore, the value of x in the triangle is approximately 14.142.