jmc

Question

The legs of a right triangle have lengths _4 27 and _2 9. If the length of the hypotenuse is h, compute 4^h.

Accepted Answer

Let t = _4 3. Then, _4 27 = 3 _4 3 = 3t, and _2 9 = _4 9_4 2 = 2 _4 31/2 = 4t. Therefore the triangle has its sides in the proportion 3:4:5, so h = 5t = 5 _4 3 = _4 243. Thus, 4^h = 243.