Question

If the area of a triangle is 96 cm, what would be the area of the triangle if the dimensions were tripled?

Answer 1

The area of a triangle is given by

`A=(b\cdot h)/(2)`

where b is the base and h the height.

If the dimensions are tripled

`\begin{gathered} b\longrightarrow3b \\ h\longrightarrow3h \end{gathered}`

then, the new area will be

`\begin{gathered} A^(\prime)=(3b\cdot3h)/(2) \\ A^(\prime)=(9b\cdot h)/(2) \end{gathered}`

which is equal to

`\begin{gathered} A^(\prime)=9((b\cdot h)/(2)) \\ \sin ce\text{ the old area A is } \\ \\ A=(b\cdot h)/(2) \\ \text{the new are is} \\ A^(\prime)=9\cdot A \end{gathered}`

In other words, the new area A' will be 9 times the old area A. Since A is equal to 96 cm^2, we get

`\begin{gathered} A^(\prime)=9\cdot96 \\ A^(\prime)=864 \end{gathered}`

that is, the new area will be 864 cm^2.