SOLUTION: . In TRIANGLE LMN, XY IS PARALLEL TO MN, area of quadrilateral XMNY= 42 sq. m. If THE RATIOS LX: XM 2: 3 ARE GIVEN, then find the area of TRIANGLE LXY. A. 28 sq. m B. 56/3 sq

Algebra ->  Geometry-proofs -> SOLUTION: . In TRIANGLE LMN, XY IS PARALLEL TO MN, area of quadrilateral XMNY= 42 sq. m. If THE RATIOS LX: XM 2: 3 ARE GIVEN, then find the area of TRIANGLE LXY. A. 28 sq. m B. 56/3 sq      Log On


   

Question 1185392: . In TRIANGLE LMN, XY IS PARALLEL TO MN, area of quadrilateral XMNY= 42 sq. m. If THE RATIOS LX: XM 2: 3 ARE GIVEN, then find the area of TRIANGLE LXY.

A. 28 sq. m
B. 56/3 sq. m
C. 8 sq. m
D. 33.6 sq. m
E. 30.7 sq. m.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Triangles LXY and LMN are similar.

With LX:XM=2:3, corresponding sides LX and LM of the two similar triangles are in the ratio LX:LM=2:5.

That means the ratio of the areas of triangles LXY and LMN is (2^2):(5^2) = 4:25.

That in turn means the ratio of the areas of LXY and XMNY is 4:21. Then, since the area of XMNY is 42 square meters...

x%2F42=4%2F21
x=8

ANSWER: The area of triangle LXY is 8 square meters. Answer choice C.

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In response to question from student....

4:25 is the ratio of the areas of the two triangles LXY and LMN.

Quadrilateral XMNY is the difference between those two triangles, so the ratio of areas of triangle LXY and quadrilateral XMNY is 4:21.