If a right triangle has side lengths of 9 and 12 how long is the hypotenuse
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that in any 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.
Applying this theorem to the given triangle, where the lengths of the two sides perpendicular to each other (the legs) are 9 and 12, respectively:
Hypotenuse^2 = Leg1^2 + Leg2^2
Hypotenuse^2 = 9^2 + 12^2
Hypotenuse^2 = 81 + 144
Hypotenuse^2 = 225
To find the length of the hypotenuse, you take the square root of both sides:
Hypotenuse = √225
Calculating the value of the square root of 225:
Hypotenuse = 15
So the length of the hypotenuse of the given right triangle is 15.