Question

$\Delta ABC\sim \Delta PQR$ and $A\left(\Delta ABC\right)=144c{m}^2$ and $A\left(\Delta PQR\right)=100c{m}^2$. If BC = 12 cm, then find the value of QR.

Answer 1

Given, $\Delta ABC\sim \Delta PQR,A\left(\Delta ABC\right)=144c{m}^2,A\left(\Delta PQR\right)=100c{m}^2$ and $BC=12cm$.
We know that,
$\frac{A\left(\Delta ABC\right)}{A\left(\Delta PQR\right)}=\frac{B{C}^2}{Q{R}^2}$ ....... (i)
Now, $\frac{A\left(\Delta ABC\right)}{A\left(\Delta PQR\right)}=\frac{144c{m}^2}{100c{m}^2}$
From (i), ${\left(\frac{BC}{QR}\right)}^2=\frac{144}{100}$
$\therefore \frac{12}{QR}=\frac{12}{10}$
$\therefore QR=10cm$.