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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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