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Delta JKL is equilateral, and Delta JKM ...

`Delta JKL` is equilateral, and `Delta JKM` is isosceles. If `bar(KL)=2`, what is the distance from L to M ?

A

`0.572`

B

`0.636`

C

`0.667`

D

`0.732`

Text Solution

Verified by Experts

The correct Answer is:
D
To get the answer to this question, you need to know about equilateral, 45-45-90, and 30-60-90 triangles. If you drop an altitude from a new point, N, through M to L, you you will divide the equilateral triangle into two 30-60-90 triangles and divide the right isosceles (or 45-45-90) triangle into two smaller right into two smaller right isosceles triangles :

Using the side ratios for 30-60-90s and 45-45-90s, you know that `bar(LN)=sqrt(3)` and that `bar(MN)=1`.
Therefore, `bar(LM)=bar(LN)-bar(MN)=sqrt(3)-1 ~~ 1.732 - 1 = 0.732`.
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