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Question


In △ ABC right-angled at B, a perpendicular is drawn from B which meets AC at M. If the ratio of areas of △ ABC and △ AMB is 9:4, find ACAB .


A
94
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B
32
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C
23
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D
49
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Solution

The correct option is B 32


‘If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other’.

By the above theorem, △ ABC is similar to △ AMB

Its given that ar(ABC)ar(AMB) =94

So, by using areas of similar triangles relation we can write,

AC2AB2=94

ACAB=32

Option b is correct.


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