Question

Let ΔABC ~ ΔDEF and their areas be respectively 64 cm² and 121 cm², then ratio of their perimeters are - *​

Answer 1

Given:-

ΔABC ~ ΔDEF

Area of ΔABC = 64cm²

Area of ΔDEF = 121cm²

To find :-

Find BC

Solution:-

$\sf\implies\dfrac{area\:of \:Triangle\:ABC}{area\:of\:Triangle\:DE F} = \dfrac{AB^2}{DE^2} = \dfrac{AC^2}{DF^2} = \dfrac{BC^2}{EF^2}$

(If two triangles are similar , ratio of their area is square of corresponding sides)

$\sf\implies\dfrac{64}{121} = \dfrac{BC^2}{EF^2}$

$\sf\implies\dfrac{8^2}{11^2}= \dfrac{BC^2}{15.4^2}$

$\sf\implies\dfrac{8}{11} = \dfrac{BC}{15.4}$

$\sf\implies BC = \dfrac {8\times 15.4}{11}$

$\sf\implies BC = 8\times 1.4$

$\sf\implies BC = 11.2$

$\Large\tt\red{Therefore\:BC\:= 11.2}$

$\huge\underline{\overline{\mid{\bold{\pink{Thanks-}}\mid}}}$