MGMAT Question Bank Geometry: 20

[Guest]

Hi all,

I came across question number 20 in the geometry question bank section and would like to see if my analysis is correct. Below is the question:

What is the length of segment BC?

(1) Angle ABC is 90 degrees.

(2) The area of the triangle is 30.

In the diagram, there is a triangle ABC, with side AB=5 and side AC=13. Side BC is not labeled. None of the 3 angles is labeled.

The answer is supposed to be A.

I wonder why statement (2) alone isn't enough to solve this question. I envision that the height of the triangle can be calculated using area=30 and a base of 13. With that, the triangle can be split into two smaller right triangles, one with hypotenuse AB=5, and other one with hypotenuse BC. x^2 + y^2 = z^2 can then be used to find the unknown side of triangle that has hypotenuse AB. With that, BC can then be eventually calculated. This method alone does not assume that angle ABC is 90 deg. Is there something wrong with this method? With this, I answered D for this question.

Thanks everyone for looking into this.

andrew

[jwinawer]

it's a good question and a VERY tricky solution. your method is almost right. the problem is that there are two different ways you can draw the triangle. i presume that the way it is drawn, once you draw the altitude from side ac to vertex b, the two sides of triangle AB and BC are on opposite sides of the altitude - one is on the left and one is on the right. in this case your method will work. BUT you can also draw a valid triangle where angle BAC is obtuse (more than 90 deg). in this case, side AB and side BC are both on the same side of the altitude. you can solve for side BC here too, but you will get a different answer. the problem is, you don't know which triangle is the right one! so you cannot answer with just statement 2.