One triangle has sides 6 cm, 8 cm and 10 cm. A second triangle has sides 15 cm, 20 cm and 25 cm. Find the area of the second triangle in ${\text{cm}}^2$.

Since $6^2+8^2=100=10^2$, the first triangle is right-angled and its area = ½ × $6\times 8=24{\text{cm}}^2$. Every side of the second triangle is 15/6 = 2.5 times as long, so the two triangles are similar with linear ratio 2.5. Areas grow as the square of that ratio: $24\times 2.$$5^2=24\times 6.25=150{\text{cm}}^2$.