BTGmoderatorDC wrote:If the lengths of the legs of a right triangle are integers, what is the area of the triangular region?
(1) The length of one leg is 3/4 the length of the other.
(2) The length of the hypotenuse is 5.
Given: The lengths of the legs of a right triangle are integers
AIDE: This is a huge piece of information. There aren't that many right triangles that have integer lengths.
Sets of 3 integers that could be the lengths of right triangles are called Pythagorean Triplets
Here are a few such triplets:
3-4-5, 5-12-13, 7-24-25, 8-15-17, etc
NOTE: It's important to remember that we can create additional triplets by multiplying each of the about triplets by some integer values.
For example, since 3-4-5 is a Pythagorean triplet, we also know that the following multiples will also be triplets:
6-8-10, 9-12-15, 12-16-20, 21-28-35 etc
Target question: What is the area of the triangular region?
Statement 1: The length of one leg is 3/4 the length of the other.
There are infinitely many right triangles that satisfy this condition.
Here are two:
Case a: A triangle has lengths 3, 4 and 5. In this case, the answer to the target question is
the area = (3)(4)/2 = 6
Case b: A triangle has lengths 6, 8 and 10. In this case, the answer to the target question is
the area = (6)(8)/2 = 24
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The length of the hypotenuse is 5
In each Pythagorean triplet, the greatest value will always represent the length of the hypotenuse.
When we examine all of the possible Pythagorean triples there are, only ONE is such that the greatest value is 5.
So statement to was telling us that the triangle must be a 3-4-5 right triangle.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
