In ∆MNO, line segment LK is parallel to NO. If the ratio of area of ∆MLK to trapezoid LKNO is 9 : 40, what is the ratio of ML to LN?

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Accepted Answer

1. Because $LK\parallel NO$, triangles $	riangle MLK$ and $	riangle MNO$ are similar.

2. Area scales by the square of the linear ratio. Let area($	riangle MLK$)=9x and trapezoid =40x, so area($	riangle MLK$)/area($	riangle MNO$)=
$9/(9+40)=9/49$.

3. Thus $(ML/MN)^2=9/49$, so $ML/MN=3/7$.

4. Then $LN=MN-ML=7k-3k=4k$. So $ML:LN=3:4$.

FINAL_ANSWER: a

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