Question

ΔABC ~ ΔDEF and their areas are respectively 64cm2 and 121 cm2. If EF = 15.4 cm., then find BC.

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)

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

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

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

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

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

$\sf\implies BC = 11.2$

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

Answer 2

Step-by-step explanation:

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}⟹

areaofTriangleDEF

areaofTriangleABC

=

DE

2

AB

2

=

DF

2

AC

2

=

EF

2

BC

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}⟹

121

64

=

EF

2

BC

2

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

11

2

8

2

=

15.4

2

BC

2

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

11

8

=

15.4

BC

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

11

8×15.4

\sf\implies BC = 8\times 1.4⟹BC=8×1.4

\sf\implies BC = 11.2⟹BC=11.2

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