Question

ΔABC ~ ΔPQR, A(ΔABC) = 80 sq.cm, A(ΔPQR) = 125 sq.cm, then complete `("A"(Δ"ABC"))/("A"(Δ"PQR")) = 80/125 = (["______"])/(["______"])`, hence `"AB"/"PQ" = (["______"])/(["______"])`

Answer 1

`("A"(Δ"ABC"))/("A"(Δ"PQR")) = 80/125` =  `16/25`  ......(i)[Given]

`("A"(Δ"ABC"))/("A"(Δ"PQR")) = "AB"^2/"PQ"^2`   .....(ii)[Theorem of areas of similar triangles]

∴ `"AB"^2/"PQ"^2 = 16/25`     .....[From (i) and (ii)]

Hence `"AB"/"PQ"` = `4/5`   ......[[Taking square root of both sides]