Problem:
If a,b>0 and the triangle in the first quadrant bounded by the coordinate axes and the graph of ax+by=6 has area 6, then ab=
Answer Choices:
A. 3
B. 6
C. 12
D. 108
E. 432
Solution:
The x-intercept of the line is a6β, and the y-intercept is b6β. Thus the area of the triangle is
21ββ
a6ββ
b6β=ab18β.
If ab18β=6, then ab=3.