Question

The altitudes of two similar triangles are 4 cm and 6 cm. If the area of the larger triangle is 36 cm², what will be the area of the other one?

Options

• 16 cm²

• 36 cm²

• 49 cm²

• 25 cm²

Answer 1

16 cm² 

Explanation:

We know,

`"Area of the larger triangle"/"Area of the smaller triangle" = ("Height of the larger" Δ)^2/("Height of the smaller" Δ)^2`

⇒ `36/"Area of the smaller triangle" = (6)^2/(4)^2`

⇒ `36/"Area of the smaller triangle" = 36/16`

∴ Area of smaller triangle = 16 cm²