Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm^2 and 121 cm^2. If EF = 15.4 cm, find

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Question 1 Let Δ ABC ~ Δ DEF and their areas be, respectively, $64 cm^2$ and $121 cm^2$. If EF = 15.4 cm, find BC.

Solution:

Given, ΔABC ~ ΔDEF

Area of ΔABC = 64 $cm^2$

Area of ΔDEF = 121 $cm^2$

EF = 15.4 cm

$\dfrac{Area \: of \: angle \: \triangle ABC}{Area \: of \: angle \: \triangle DEF} = \dfrac{AB^2}{DE^2}$

As we know, if two triangles are similar, ratio of their areas are equal to the square of the ratio of their corresponding sides

⇒ $\dfrac{AC^2}{DF^2} = \dfrac{BC^2}{EF^2}$

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

$(\dfrac{8}{11})^2 = (\dfrac{BC}{15.4})^2$

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

BC = 8×$\dfrac{15.4}{11}$

BC = 8 × 1.4

BC = 11.2 cm

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