Question

Two triangles have bases with lengths 5in and 8in. What is the ratio of the areas of the triangles? If the smaller triangle is 15in², what is the area of the larger triangle?

Answer 1

`\begin{gathered} \text{Triangle area =}(base\cdot high)/(2) \\ AreaTriangle\text{ }1=(5\cdot high)/(2)=2.5\text{high} \\ \\ AreaTriangle\text{ }2=(8\cdot high)/(2)=4\text{high} \\ \\ ratio=\frac{AreaTriangle\text{ }2}{AreaTriangle\text{ }1} \\ \\ S\text{upposing both triangles have the same high} \\ ratio=\frac{4\text{high}}{2.5\text{high}}=1.6 \\ The\text{ ratio of areas is 1.6} \\ \\ \text{If the smaller triangle is 15 in}^2 \\ ratio=\frac{AreaTriangle\text{ }2}{AreaTriangle\text{ }1} \\ \\ AreaTriangle\text{ }2=ratio\cdot AreaTriangle\text{ }1 \\ AreaTriangle2=1.6\cdot\text{15 in}^2 \\ AreaTriangle2=\text{ 24 in}^2 \\ \text{The area of the larger triangle is 24 in}^2 \end{gathered}`