Chapter 4.7, Problem 2PT

A carpenter has a 10-foot-long board to mark off a triangular area on the floor in the corner of a room. See the figure. What is the function for the triangular area in terms of x that may be used to determine the maximum such area?

1. a) $A=\frac{1}{2}{x}^2$
2. b) $A=\frac{1}{2}(x^2+10)$
3. c) $A=\frac{1}{2}x\sqrt{100-x^2}$
4. d) $A=\frac{1}{2}x\sqrt{100-2x^2}$