Question

If the areas of two similar triangles are in the ratio 361:529. What would be the ratio of the corresponding sides?

(a) 19 : 23

(b) 23 : 19

(c) 361 : 529

(d) 15 : 23

I got this question in a national level competition.

My query is from Area of Similar Triangle in chapter Triangles of Mathematics – Class 10

Answer 1

Right choice is (a) 19 : 23

The best I can explain: We know that the ratio of areas of similar triangles is equal to the ratio of the squares of their corresponding sides.

Here the ratio of areas of two similar triangles is 361:529.

     

According to the theorem,

\(\frac {area \, of \, triangle \, \triangle ABC}{area \, of \, triangle \, \triangle DEF}=(\frac {AB}{DE})\)^2

\(\frac {361}{529}=(\frac {AB}{DE})\)^2

\(\sqrt {\frac {361}{529}}=\frac {AB}{DE}\)

\(\frac {AB}{DE}=\frac {19}{23}\)