In the Fig. below, 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 ΔJAB?
Solution
Given: JKLM is a square with sides of length 6units. 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
To find: Probability that the point will be chosen from the interior of ΔJAB.
We the following figure
Area of square JLKM is equal to
= `6^2`
= 36 sq units
Now we have
`area(triangleKAJ)= 1/2xxAKxxKJ`
`=1/2xx3xx6`
=9 units2
`area(triangleJMB)=1/2xxJMxxBM`
`=1/2xx6xx3`
=9/2 units2
Now area of the triangle AJB
`area(triangleAJB) = 36-9-9-9/2`
=`27/2`units2
We know that Probability
=`"Number of favourable event"/"Total number of event"`
`= (27/2)/36`
`= 27/(2xx36)`
`= 3/8`
Hence the Probability that the point will be chosen from the interior of ΔAJB is `3/8`.
