Question

The length of a pair of corresponding sides of two similar ∆'s are 3 cm and 11 cm. If the area of the first ∆ is 18 cm^2 find the area of the second ∆.​

Answer 1

The area of the second triangle is 242 cm²

Explanation:

In the similar triangles

• The ratio between their perimeters equals the ratio between their corresponding sides

• The ratio between their areas equals square the ratio between their corresponding sides

∵ The length of a pair of corresponding sides of two similar ∆'s are

3 cm and 11 cm

→ Find the ratio of the corresponding sides

∴ The ratio of their corresponding sides =
`(3)/(11)`

∵ The area of the first ∆ is 18 cm²

→ Use the second rule above

∵
`(A1)/(A2)` =
`((3)/(11)) ^(2)`

∵ A1 = 18 cm²

→ Substitute it in the ratio above

∴
`(18)/(A2)` =
`(9)/(121)`

→ By using the cross multiplication

∵ A2 × 9 = 18 × 121

∴ 9A2 = 2178

→ Divide both sides by 9

∴ A2 = 242 cm²

∴ The area of the second triangle is 242 cm²