Question

The areas of two similar triangles are 16cm² and 9cm² respectively. If the altitude of the smaller triangle is 1.8cm, find the length of the altitude corresponding to the larger triangle.

Answer 1

The ratio of the areas of two similar triangles is equal to the ratio of the square of the corresponding altitudes.

∴ `("area"(Δ"ABC"))/("area"(Δ"PQR")) = "AL"^2/"DM"^2`

⇒ `(16)/(9) = "AL"^2/1.8^2`

⇒ AL² = `(16 xx 3.24)/(9)`

⇒ AL² = 5.76
⇒ AL = 2.4cm.