Question

In the figure, JKLM is a square with sides of length $6$ units. Points A and B are the mid-points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of $\Delta$ JAB?

Answer 1

$JKLM$ is a square with sides of length $6$ units. Points $A$ and $B$ are the midpoints of sides $KL$ and $ML,$ respectively. If a point is selected at random from the interior of the square.

We have to find the probability that the point will be chosen from the interior of $△JAB$.

Now,

Area of square $JKLM$ is equal to $6^2=36$ sq.units

Now, we have

$ar\left(△KAJ\right)=\frac{1}{2}\times AK\times KJ$

$=\frac{1}{2}\times 3\times 6=9$sq.unit

$ar\left(△JMB\right)=\frac{1}{2}\times JM\times BM$

$=\frac{1}{2}\times 6\times 3=9$sq.unit

$ar\left(△AJB\right)=36-9-9-\frac{9}{2}=18-\frac{9}{2}=\frac{36-9}{2}=\frac{27}{2}$sq.units.

We know that probability$=\frac{Numberoffavourableevent}{Totalnumberofevent}$

$=\frac{\frac{27}{2}}{36}=\frac{27}{2\times 36}=\frac{3}{8}$

Hence the probability that the point will be chosen from the interior of $△AJB$ is $\frac{3}{8}$