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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 ∆.​

User Hvqzao
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1 Answer

11 votes

Answer:

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

User Hafiz Mujadid
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