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Question

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

A
4 : 5
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B
5 : 4
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C
3 : 2
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D
5 : 7
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Solution

The correct option is A 4 : 5
Let the required triangle be ΔABCandΔPQR
with A=P

So ΔABC is similar to ΔPQR
(By SAS similarity)

Let the altitude of two triangles be AD and PS
So The ratio of the areas of two similar triangle is equal to the square of ratio of their corrosponding altitudes.

ar(ΔABC)ar(ΔPQR)=AD2PS2

1625=AD2PS2

ADPS=45=4:5

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