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

Answer:

The area of the second triangle is 242 cm²

Step-by-step 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 = $\frac{3}{11}$

∵ The area of the first ∆ is 18 cm²

→ Use the second rule above

∵ $\frac{A1}{A2}$ = $(\frac{3}{11}) ^{2}$

∵ A1 = 18 cm²

→ Substitute it in the ratio above

∴ $\frac{18}{A2}$ = $\frac{9}{121}$

→ 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