Question

If $\Delta ABC\sim \Delta PQR$ and $\frac{PQ}{AB}=\frac{5}{2}$ then area $\left(\Delta ABC\right):$ area $\left(\Delta PQR\right)=?$

• A. $25:4$
• B. $4:25$
• C. $5:2$
• D. $25:2$

Answer 1

Answer: (B)

$4:25$

Given that, $\Delta ABC\sim \Delta PQR$

Also, $\frac{PQ}{AB}=\frac{5}{2}$

To find out: Ratio of the areas of the two triangles.

We know that, if triangles are similar, then the ratio of their areas is equal to the square of the ratio of their sides.

$\therefore \frac{area\left(ABC\right)}{area\left(PQR\right)}={\left(\frac{AB}{PQ}\right)}^2$

$={\left(\frac{2}{5}\right)}^2[\because \frac{PQ}{AB}=\frac{5}{2}\Rightarrow \frac{AB}{PQ}=\frac{2}{5}]$.

$=\frac{4}{25}$

Hence, the required ratio is $4:25$.