In a certain isosceles right triangle, the altitude to the hypotenuse has length 6. What is the hypotenuse of the triangle?
We have the following relationship
(1/2) length of hypotenuse / 6 = 6 / (1/2) length of hypotenuse
cross - multiply
[ (1/2)lengt of hypotenuse ] ^2 = 6 * 6
[ (1/2) length of hypotenuse ] ^2 = 36 take the postive root of both sides
(1/2) length of hypotenuse = 6
So
Length of hypotenuse = 2 * 6 = 12