Question

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

Answer 1

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