Question

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

Answer 1

Given: A square dart board is shown. The length of a side of the larger square is 1.5 times the length of a side of the smaller square. If a dart is thrown and lands on the larger square

To find: Probability that it will land in the interior of the smaller square Let the length of smaller square is x cm Therefore the length of side of bigger square will be 1.5x cm

Area of bigger square `=(1.5x)^2 `

`= 2.25x^2 cm^2`

Area of smaller square`=x^2cm^2`

We know that Probability`="Number of favourable event"/"Total number of event"`

Hence probability that the dart will land in the interior of the smaller square is equal to `=x^2/(2.25x^2)=4/9`