Question

The areas of two similar triangles are 16 cm2 and 25 cm2. One of the sides of the first triangles is 2 cm. What is the length of the corresponding side of the other triangle?

Answer 1

The length of the corresponding side is 2.5 cm

Explanation:

∵ The 2 Δ are similar

∴ Their sides are proportional

∵ The area of first Δ 16 cm²

∵ The area of second Δ 25 cm²

∵ One side of first Δ 2 cm

∵ From similarity
`((S1)/(S2))^(2)=(A1)/(A2)`

∴
`((2)/(S2))^(2)=(16)/(25)`

∴
`(2)/(S2)=\sqrt{(16)/(25)}`

∴
`(2)/(S2)=(4)/(5)`

∴
`S2=((5)(2))/(4)=2.5` cm