Question

ΔABC ∼ ΔDEF and A(ΔABC) : A Δ(DEF) = 1 : 2 If AB = 4 find DE.

Answer 1

(1) Δ ABC ∼ Δ DEF
`(A(DeltaABC))/(A(DeltaDEF)) = (AB)^2/(DE)^2`

`1/2 = 4^2/(DE^2)`

`1/2 = 16/(DE^2)`

∴ `DE^2 = 16 × 2 ∴ DE = 4sqrt2`