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Home » ∆ABC~∆DEF such that ar(∆ABC) = 36 and ar(∆DEF) = 49 . Then, the ratio of their corresponding sides is (a) 36 : 49 (b) 6 : 7 (c) 7 : 6 (d) √6 : √7
∆ABC~∆DEF such that ar(∆ABC) = 36 c{m^2} and ar(∆DEF) = 49 c{m^2}. Then, the ratio of their corresponding sides is (a) 36 : 49 (b) 6 : 7 (c) 7 : 6 (d) √6 : √7
CBSE | Class 10 | Exercise MCQ | Maths | RS Aggarwal | Triangles
∆ABC~∆DEF such that ar(∆ABC) = 36 c{m^2} and ar(∆DEF) = 49 c{m^2}. Then, the ratio of their corresponding sides is (a) 36 : 49 (b) 6 : 7 (c) 7 : 6 (d) √6 : √7

Correct Answer: (b) 6:7

Explanation:

In ∆ABC ~ ∆DEF,

\begin{array}{l} \frac{{AB}}{{DE}} = \frac{{BC}}{{EF}} = \frac{{AC}}{{DF}}\\ \frac{{ar(\Delta ABC)}}{{ar(\Delta DEF)}} = \frac{{A{B^2}}}{{D{E^2}}}\\ \frac{{36}}{{49}} = \frac{{A{B^2}}}{{D{E^2}}}\\ \frac{6}{7} = \frac{{AB}}{{DE}}\\ \frac{{AB}}{{DE}} = \frac{{BC}}{{EF}} = \frac{{AC}}{{DF}} = \frac{6}{7} \end{array}

The ratio of corresponding sides is 6 : 7.

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