Exams › SSC CGL (Prelims) › General

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

1. 3: 4
2. 3: 7
3. 4: 5
4. 4: 9

Correct answer: 3: 4

Solution

Because \(LK \parallel NO\), triangles \(MLK\) and \(MNO\) are similar. If the area ratio of small triangle to trapezoid is 9:40, then the area ratio of small triangle to whole triangle is 9:(9+40)=9:49, so the side ratio is 3:7. Therefore, \(ML:MN=3:7\), giving \(ML:LN=3:(7-3)=3:4\).

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