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Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 121 cm^2. If EF = 15.4 cm, find BC - Mathematics

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Sum

Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC

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Solution

It is given that ΔABC ~ ΔDEF

`:. (ar(triangleABC))/(ar(triangleDEF)) = ((AB)/(DE))^2 = ((BC)/(EF))^2=((AC)/(DF))^2`

Given that

EF = 15.4

ar(ΔABC) = 64 cm2

ar(ΔDEF) = 121 cm2

`:.(ar(ABC))/(ar(ΔDEF))=((BC)/(EF))^2`

`=>((64 cm^2)/(121 cm^2)) = (BC^2)/(15.4 cm)^2`

`=>(BC)/15.4 = (8/11)cm`

`=>BC = ((8xx15.4)/11)cm = (8 xx 1.4) cm = 11.2 cm`

Concept: Areas of Similar Triangles
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APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.4 | Q 1 | Page 143

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