Two isosceles triangles have equal angles and their areas are in the ratio of 16 : 25, then the ratio of their corresponding heights is …
Two isosceles triangles have equal angles and their areas are in the ratio of 16 : 25, then the ratio of their corresponding heights is ……………
(A) 4 : 5
(B) 5 : 4
(C) 3 : 2
(D) 1 : 4
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Correct option is (A) 4 : 5
Two isosceles triangles have equal angles.
Then these isosceles triangles are similar triangles.
We know that the area of similar triangles are in the ratio of the squares of their corresponding heights.
\(\therefore\) Ratio of corresponding height of similar triangle
= (Ratio of areas of similar triangle\()^\frac12\)
\(=(\frac{16}{25})^\frac12\) \(=\frac{\sqrt{16}}{\sqrt{25}}\)
\(=\frac45\) = 4 : 5
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