AbeNeedsAnswers wrote:
In triangle JKL shown above, what is the length of segment JL ?
(1) JK = 10
(2) KL = 5
D
Source: Official Guide 2020
KEY CONCEPT: 30-60-90 triangles are known as special right triangles, and we know quite a bit about this kind of triangle
Target question: What is the length of segment JL ?
Statement 1: JK = 10
Compare ΔJKL with the
BASE 30-60-90 triangle.
Their corresponding hypotenuses are
10 and
2, which tells us that ΔJKL is
5 times the size of
BASE 30-60-90 triangle.
So, the length of
segment JL will be
5 times the size its corresponding side (with length
√3)
In other words,
JL must have length 5√3
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: KL = 5
The corresponding sides here have lengths
5 and
1, which tells us that ΔJKL is
5 times the size of
BASE 30-60-90 triangle.
So,
JL must have length 5√3
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
