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Home » Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25: 36. The ratio of their corresponding heights is (a) 25 : 36 (b) 36 : 25 (c) 5 : 6 (d) 6: 5
Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25: 36. The ratio of their corresponding heights is (a) 25 : 36 (b) 36 : 25 (c) 5 : 6 (d) 6: 5
CBSE | Class 10 | Exercise MCQ | Maths | RS Aggarwal | Triangles
Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25: 36. The ratio of their corresponding heights is (a) 25 : 36 (b) 36 : 25 (c) 5 : 6 (d) 6: 5

Correct Answer: (c) 5:6

Explanation:

Let x and y be the corresponding heights of the two triangles.

The corresponding angles of the triangles are equal.

The triangles are similar. (By AA criterion)

\begin{array}{l} \frac{{ar({\Delta _1})}}{{ar({\Delta _2})}} = \frac{{25}}{{36}} = \frac{{{x^2}}}{{{y^2}}}\\ \frac{{{x^2}}}{{{y^2}}} = \frac{{25}}{{36}}\\ = > \sqrt {\frac{{25}}{{36}}} \\ = > \frac{5}{6}\\ = > 5:6 \end{array}

 

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