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What is the area of right triangle ABC?

This topic has 2 expert replies and 0 member replies

What is the area of right triangle ABC?

Post Tue Sep 12, 2017 5:09 am
What is the area of right triangle ABC?

(1) Side AB measures 5 meters and Side BC measures 13 meters

(2) Angle ABC measures 90 degrees.

Looking for a correct solution for their answer.

OA: C

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Post Tue Sep 12, 2017 9:10 am
This question asks about solving for the area of a right triangle. We'll need to know that the area of a triangle is A = (1/2)bh. This means that if we know that base and the height of the triangle, we can solve for the area. Let's look at each statement individually.

Statement 1

This statement tells us the length of two sides of the triangle: AB and BC. However, it doesn't tell us what the relationship between the two sides is - are they the base and the height? The base and the hypotenuse? The height and the hypotenuse? So the triangle might look like this:

ttps://postimg.org/image/yjjuv1qmt/" target="_blank">

Or it might look like this:

ttps://postimg.org/image/7csd3dt79/" target="_blank">

The two triangles will have different bases and, thus, different areas. Statement 1 is insufficient.

Statement 2

This statement tells us that angle ABC is 90 degrees. This tells us nothing about the lengths of the sides: the triangle could be really, really small or really, really big. Statement 2 is insufficient.

BOTH

Putting the statements together, we know that if angle ABC is 90 degrees, AB and BC are the sides adjacent to the 90 degree angle - the base and the height of the triangle. This means we can solve for area by plugging 5 and 13 into the area formula.

A = (1/2)*5*13

BOTH statements together are sufficient. The correct answer is C.

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Top Reply
Post Tue Sep 12, 2017 9:09 am
Hi ardz24,

We're told that triangle ABC is a RIGHT triangle. We're asked for the area of the triangle. To answer this question, we'll need to know the base and the height of the triangle.

1) Side AB measures 5 meters and Side BC measures 13 meters

Since we don't know the 'orientation' of the triangle, we don't know which two sides are represented by the information in Fact 1. If those two sides are the 'short' sides, then the area of the triangle is (1/2)(5)(13) = 32.5. However, if the hypotenuse of the triangle is the 13, then the 'other' short side is 12 (a 5/12/13 right triangle) and the area is (1/2)(5)(12) = 30.
Fact 1 is INSUFFICIENT

2) Angle ABC measures 90 degrees.

Fact 2 defines the angle that is the 90 degree angle, but does not give us any measurements to work with.
Fact 2 is INSUFFICIENT

Combined, we know which angle is the 90 degree angle and that the two sides mentioned in Fact 1 must be the two 'short' sides. Thus, the answer to the question is (1/2)(5)(13) = 32.5
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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