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Solution for If triangle Abc ~ triangle Def Such that Ab = 5 Cm, Area (triangle Abc) = 20 Cm2 and Area (triangle Def) = 45 Cm2, Determine De. - CBSE Class 10 - Mathematics

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Question

If ΔABC ~ ΔDEF such that AB = 5 cm, area (ΔABC) = 20 cm2 and area (ΔDEF) = 45 cm2, determine DE.

Solution

We have,

ΔABC ~ ΔDEF such that AB = 5 cm,

Area (ΔABC) = 20 cm2 and area(ΔDEF) = 45 cm2

By area of similar triangle theorem

`("Area"(triangleABC))/("Area"(triangleDEF))="AB"^2/"DE"^2`

`rArr20/45=5^2/"DE"^2`

`rArr4/9=5^2/"DE"^2`

`rArr2/3=5/"DE"`                   [Taking square root]

`rArr"DE"=(3xx5)/2=7.5` cm

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Solution If triangle Abc ~ triangle Def Such that Ab = 5 Cm, Area (triangle Abc) = 20 Cm2 and Area (triangle Def) = 45 Cm2, Determine De. Concept: Areas of Similar Triangles.
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