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In figures triangle ABC and triangleDEF ...

In figures `triangle ABC and triangleDEF` ar similar , the areas of `triangle ABC` is 9 sq. m and that of `triangleDEF` is 16 sq. cm. if EF= 4.2 cm, find BC.

Text Solution

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ar`(triangleABC)= 9 sq.cm`
`ar triangle(DEF) = 16 sq.c m`
EF=4.2 cm
BC= ?
Since the ratio of areas of two similar triangles is equal to ratio of square on their corresponding sides
` ( ar(triangleABC))/(ar(triangleDEF))= (BC^(2))/(EF^(2))`
`Rightarrow 9/16 = ((BC)/(EF))^(2)`
`(BC)/(4.2)= 3/4`
`Rightarrow BC= (3xx 4.2)/4= 3.15 cm `
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