Problem 1

Given information

A right triangle is given with one of its leg cm. One needs to express the altitude as the function of the hypotenuse.

Step-by-step explanation

Suppose is the length of the hypotenuse of the right triangle, is the length of altitude, and is the length of the other leg. 

If one looks into the area of the triangle, then the area will be  when considering the hypotenuse as a base and altitude as a height, and the area will be when considering the perpendicular leg as a height and leg of length cm as a base. Thus one will get an equation by equating both the areas. That is, .