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Question

Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Find the ratio of their corresponding heights. [4 MARKS]


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Solution

Concept : 1 Mark
Application : 2 Marks
Calculation : 1 Mark

Let ΔABC and ΔDEF be the given triangles in which

AB=AC,DE=DF,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]

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 height = 4 : 5 .


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