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}}=((5)/(3))^2=(25)/(9)`

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

`\frac{area\text{ larger triangle}}{\text{6}0}=(25)/(9)`

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

`\text{area large triangle = 60( }(25)/(9))`

which gives

`\begin{gathered} \text{area large triangle = 60( }(25)/(9)) \\ \text{area large triangle = }(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