Question

Two similar triangles have a ratio of 3cm:5cm. The smaller triangle has an area of 60 cm2. What is the area of the larger triangle?

Answer 1

By applying the area of similar triangles theorem, we can write

$\frac{area\text{ larger triangle}}{\text{area small triangle}}=(\frac{5}{3})^2=\frac{25}{9}$

since the area of the small triangle is 60 cm^2, we have

$\frac{area\text{ larger triangle}}{\text{6}0}=\frac{25}{9}$

If we move 60 to the right hand side, we get

$\text{area large triangle = 60( }\frac{25}{9})$

which gives

$\begin{gathered} \text{area large triangle = 60( }\frac{25}{9}) \\ \text{area large triangle = }\frac{1500}{9} \\ \text{area large triangle = 1}66.66 \end{gathered}$

that is, the area of the larger triangle is equal to 166.66 cm^2