A Couple of Geometric Triangle Problems

1. One of the legs of a right triangle has the length of 4 cm. Express the length of the altitude (h) perpendicular to the hypotenuse (c) as a function of the length of the hypotenuse. (Label the additional leg as b) Make a sketch to support the given information before working the problem.

2. The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse (c) as a function of the perimeter (P). Make a sketch to support the given information before working the problem.