Question

In the fig $13.13$, a square dart board is shown. The length of a side of the lager square is $1.5$times the length of a side of the smaller square. If a dart is thrown and land on the larger square. What is the probability that it will land in the interior of the smaller square?

Answer 1

Let $ABCD$ & $PQRS$

be $2$ square

(figure not made according to scale)

Let $PQ=S$

$\therefore$ according to question

$AB=1.5\left(PQ\right)$

$=1.5S=\frac{3}{2}S$

area of square $ABCD={\left(\frac{3}{2}S\right)}^2$

$=\frac{9}{4}{S}^2$

area of square $PQRS=S\times S$

$=S^2$

$\therefore$ Probability that dost will land in

smaller square $=\frac{areaofPQRS}{areaofABCD}$

$=\frac{S^2}{\left(\frac{9}{4}{S}^2\right)}$

$=\frac{S^2}{S^2}\left(\frac{4}{9}\right)$

$=\frac{4}{9}$

$=\left(0.44\right)$