Question

A ABC and A DEF are similar and
AB=1/3DE, then find ar (s ABC):
ar (A DEF).​

Answer 1

ar ( △ABC) : ar(△DEF) = 1 : 9

Given :-

ABC and DEF are two similar △'s.

AB = $\large\frac{1}{3}$DE

To find:-

ar (△ABC) : ar (△DEF)

Solution:-

Since, △ABC and △DEF are two similar triangles.(Given)

We know that,

The ratio of the areas of the two similar triangles is equal to the ratio of the squares of their corresponding sides. (Theorem)

By using this theorem,

$\bold{\frac{ar(ABC)}{ar(DEF)} = \frac{ {AB}^{2} }{ {DE}^{2} } }$

We have, AB = 1/3 DE

DE = 3AB ; put Value of DE

then,

$\bold{ \frac{ar(ABC)}{ar(DEF)} = \frac{ {AB}^{2} }{ {(3AB)}^{2} } }$

$\bold{\frac{ar(ABC)}{ar(DEF)} = \frac{ {AB}^{2} }{ {9AB}^{2} } }$

cancel out AB².

$\bold{ \frac{ar(ABC)}{ar(DEF)} = \frac{1}{9} }$

hence, the ratio of the area of △ABC and △DEF is 1 : 9 .