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Question
Two isosceles triangle have equal vertical angles and their areas are in the ratio of 36 : 25. Find the ratio between their corresponding heights.
Solution
ΔABC and ΔPQR be the two isosceles triangles such that
∠A = ∠P.
Then ΔABC ∼ ΔPQR.
Let AD and PS be their height then
`"area (ΔABC)"/"area (ΔPQR)" = "AD"^2/"PS"^2`
⇒ `(36)/(25) = "AD"^2/"PS"^2`
⇒ `"AD"/"PS" = (6)/(5)`
⇒ AD : PS = 6 : 5.
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