Question

Sides of two similar triangles are in the ratio 5:11 then ratio of their areas is
A. 25:11
B. 25:121
C. 125:121
D. 121:25

Answer 1

Hint-We should use the property of similar triangles which tells if the sides of two similar triangles is in the ratio a:b then their areas would be in the ratio ${a^2}:{b^2}$ to solve such type of questions.

Complete step-by-step answer:
We know the property of similar triangles which tells if the sides of two similar triangles is in the ratio a:b then their areas would be in the ratio ${a^2}:{b^2}$
i.e Ratio of area of two similar triangles = ratio of square of corresponding sides
$ \Rightarrow $ Ratio of the sides = 5 : 11
$\begin{gathered}
  \therefore {\text{Ratio of areas = }}{{\text{5}}^2}:{11^2} \\
   = 25:121 \\
\end{gathered} $

Note- The Area Ratio Theorem holds true for two similar triangles with corresponding sides in proportion . Unlike congruent triangles which have the same area , similar triangles have areas and sides in a fixed ratio .