Find the length of each leg of an isosceles right triangle whose hypotenuse =12

Answer 1

An isosceles right triangle is also a 45-45-90 right triangle. In this type of right triangle, the hypotenuse is always the product of the leg and the square root of 2. So to find the length of each leg, just divide the hypotenuse, 12 , by the square root of 2. Then to remove the radical from the denominator, multiply both numerator and denominator by square root of 2. This then leaves you with [12 (square root of 2)]/2 which reduces to 6(square root of 2).

Answer 2

the hypotenuse of an isosceles right triangle is equal to the measure of the leg times √2

let n=length of a leg

hypotenuse=n√2

12=n√2

square both sides

144=2n^2

72=n^2

take the square root of both sides

n=√72

n=√(36*2)

n=√36√2

n=6√2

you can get the same answer using the Pythagorean Theorem

n^2+n^2=12^2

2n^2=144

n^2=72

n=√72

n=6√2