This question asks us to determine whether or not we can solve for the area of triangle
ABC. We should recognize that we will probably be dealing with the equation for area of a triangle:
A = 1/2(bh). If we can solve this equation, we can solve the problem.
Statement 1
We know that
BD is the height of our triangle and that
AC is the base of our triangle. So the product of
BD and
AC =
bh = 20. This means that we could plug 20 in for
bh in our area equation to solve for
A.
Statement 1 is sufficient. We can eliminate answers B, C, and E.
Statement 2
If
x = 45, we know that
ABD is a 45-45-90 triangle, which means that angle
ABD is also 45 degrees and that
AD = BD. However, we still don't know a bunch of things.
- We don't know how long AD and BD are-they could both be 1 unit long, they could both be 100 units long, they could both be 1000 units long. BD is our height and AD is part of our base, so changing these numbers has a pretty big impact on area.
- We don't know anything about the length of CD-the other half of our base. It's easy to assume based on the diagram that angle BCD is 45 degrees, and thus CD is the same length as AD ... but we don't actually know that. CD could be way longer or way shorter than AD. Again, changing this length changes our base and thus changes area.
Statement 2 is NOT sufficient. A is correct.
