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Question

Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is ____.

A
16:25
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B
25:16
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C
4:5
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D
5:4
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Solution

The correct option is C 4:5

Let ΔABC and ΔDEF be the given triangles in which

AB=AC,DE=DF and A=D

Draw ALBC and DMEF



Now, ABAC=1 and DEDF=1
(∵ AB = AC and DE = DF)

ABAC=DEDF

ABDE=ACDF.....(1)

In ΔABC and ΔDEF,

ABDE=ACDF [ From (1)]

and A=D

ΔABCΔDEF (by SAS similarity criterion)

But, the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding heights.

Area (ΔABC)Area (ΔDEF)=AL2DM2

1625=(ALDM)2

ALDM=45

AL : DM = 4 : 5 , i.e, the ratio of their corresponding heights is 4 : 5 .


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