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

Answer:

The length of the corresponding side is 2.5 cm

Step-by-step 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 $(\frac{S1}{S2})^{2}=\frac{A1}{A2}$

∴ $(\frac{2}{S2})^{2}=\frac{16}{25}$

∴ $\frac{2}{S2}=\sqrt{\frac{16}{25}}$

∴ $\frac{2}{S2}=\frac{4}{5}$

∴ $S2=\frac{(5)(2)}{4}=2.5$ cm