One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse?
5^2 + 5^2 = h^2
To find the length of the hypotenuse of an isosceles right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, one leg of the triangle measures 5 inches. Since an isosceles right triangle has two congruent legs, the other leg must also measure 5 inches. Let's call the length of the hypotenuse "c".
So, we can use the Pythagorean theorem equation:
c^2 = 5^2 + 5^2
Simplifying:
c^2 = 25 + 25
c^2 = 50
To find the length of the hypotenuse, we need to find the square root of 50.
c ≈ √50
Using a calculator, we find that √50 ≈ 7.07.
Therefore, rounded to the nearest tenth, the approximate length of the hypotenuse is 7.1 inches.