Question

The base of triangle is $8\mathrm{meters}$. The base of a similar triangle $Q$ is $7\mathrm{meters}$.What is the value of the ratio of the area of $P$ to the area of $Q$?

Answer 1

Find the ratio of the area of figure $P$ to the area of figure $Q$.

Given, the base of triangle $P$ is $8\mathrm{meters}$

The base of triangle $Q$ is $7\mathrm{meters}$.

Since, when two figure then the value of the ratio of their perimeter is equal to the value of their corresponding side lengths.

$\Rightarrow \frac{AreaoffigureP}{AreaoffigureQ}=\frac{{(BaseoffigureP)}^2}{{(BaseoffigureQ)}^2}$

So, the ratio of figure $A$ to figure $B$ is

$$\begin{gathered} \Rightarrow \frac{AreaoffigureP}{AreaoffigureQ}=\frac{8^2}{7^2} \\ \Rightarrow \frac{AreaoffigureP}{AreaoffigureQ}=\frac{64}{49} \end{gathered}$$

Hence, the ratio of the area of figure $P$ to the area of figure $Q$ is $\frac{64}{49}$.