Triangle

IMO you don't really have to do any math to solve this problem.

1) tells you the height of the triangle is 8.
PO = 10 since it would be a 6-8-10 right triangle made with the partial base.

lets say for a minute that the area of the triangle = 48.

for the area = 48, you need base = 12. (1/2)(8)(12) = 48.

we know the fixed height = 8, it would be an additional 6 for the base = 12, and PQ = 10.

but they say PQ>PO which means PQ > 10 which mean that additional base would be > 6 since height is constant.

we know from this that the base > 12 which would make area > 48. SUFFICIENT.

2) We are given the entire base, but not height. Insufficient.

(A)

ssmiles08 wrote:IMO you don't really have to do any math to solve this problem.

1) tells you the height of the triangle is 8.
PO = 10 since it would be a 6-8-10 right triangle made with the partial base.

lets say for a minute that the area of the triangle = 48.

for the area = 48, you need base = 12. (1/2)(8)(12) = 48.

we know the fixed height = 8, it would be an additional 6 for the base = 12, and PQ = 10.

but they say PQ>PO which means PQ > 10 which mean that additional base would be > 6 since height is constant.

we know from this that the base > 12 which would make area > 48. SUFFICIENT.

2) We are given the entire base, but not height. Insufficient.

(A)

I was able to get the statement 1. But my question was more about the statement 2.
now its true that only the base is given. But how can you be sure that the area will not always be less than or greater than 48 when PO<PQ?

if you want to take a simple example to disprove statement 2, you can make triangle OPQ a 5-12-13 right triangle.

OP = 5, PQ = 12, OQ = 13. PQ > OP so it satisfies the question stem.

area of this triangle = 6*5 = 30 < 48.

similarly we can take point P (6,8) and base = 13 to make area > 48 like in statement 1.

-hope that helps.