Write the area A of the triangle as a function of x, and determine the domain of the function.

Question

A right triangle is formed in the first quadrant by the x- and y-axes, from (0,y) and (x,0) and a line through the point (5, 3). Write the area A of the triangle as a function of x, and determine the domain of the function. (Enter your answer for the domain using interval notation.)

Answer 1

One way to answer this question is the following:

y = [(3-b)/5]x + b where b is greater than 3.

This is a family of lines with negative slope as required and passes through the point (5,3).

The area of the triangle is (b/2)[-5b/(3-b)].