Question

ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144 : 81, then AB : DE = ?

Answer 1

`(A(ΔABP))/(A(ΔDEF)) = 144/81`   ...(i)[Given]

`(A(ΔABP))/(A(ΔDEF)) = (AB^2)/(DE^2)`   ...(ii)[Theorem of areas of similar triangles]

∴ `(AB^2)/(DE^2) = 144/81`   ...[From (i) and (ii)]

∴ `(AB)/(DE) = 12/9` or `4/3`   ...[Taking square root of both sides]