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 a6​, and the y-intercept is b6​. Thus the area of the triangle is
21​⋅a6​⋅b6​=ab18​.
If ab18​=6, then ab=3.