Unable to get right answer

[Motherof8]

This is a geometry problem, but I had to use Algebra too. The book states the problem this way:

In right triangle JKL, angle JKL is the right angle, and KH is perpendicular to JL. If KH = 12, and HL = 40, we are told to find JK, and to assume that JK is the shorter leg of right triangle JKL.

I drew a right triangle and labeled the top vertex L, the one on the right angle K, and the other one J. I drew a line from K to the middle of line JL, and labeled the end H.

The book gives the answer as 4 times the square root of 10, but I don't get that answer when I work it out. I used the Pythagorean theorem for both triangles. I made 2 formulas: x squared + x squared = 1,600. 144 + x squared = x squared. I got x squared = 872.

What am I doing wrong?

[stapel_eliz]

You need to simplify your answer, but I think you're right; the book is wrong.