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In the 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?
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Given:
In the 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.
A dart is thrown and lands on the larger square.
To do:
We have to find the probability that it will land in the interior of the smaller square.
Solution:
Let the length of the side of the smaller square be $a$ units.
This implies,
The length of the side of the square $\mathrm{ABCD}=1.5 \times a$ units
$=\frac{3}{2}a$ units.
Area of square $\mathrm{ABCD}=(\frac{3 a}{2})^{2}$
$=\frac{9}{4} a^{2}$ sq. units.
Area of square $\mathrm{PQRS}=a^{2}$ sq. units
Probability that it will land in the interior of the smaller square $=\frac{a^{2}}{\frac{9}{4} a^{2}}$
$=a^{2} \times \frac{4}{9 a^{2}}$
$=\frac{4}{9}$
The probability that it will land in the interior of the smaller square is $\frac{4}{9}$.
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