Jklm is a square with sides …
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Jklm is a square with sides of length 6unit . Point A and B are the midpoint of side kl and lm respectively. If a point is selected at random from the interior of the square . What is probability that the point will be chosen from the interior of ∆ jab
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Sia ? 6 years, 6 months ago
Side of square {tex}= 6\ units{/tex}
Since A and B are the mid-point of KL and LM,
{tex}KA = AL = LB =BM = 3 units{/tex}
{tex}\therefore{/tex}Area of square = {tex}6 \times 6 = 36\ sq. units{/tex}
Area of {tex}\triangle{/tex}AJB = area of square - area of {tex}\triangle{/tex}AKJ - area of {tex}\triangle{/tex}BMJ - Area of {tex}\triangle ALB{/tex}
=36 - {tex}\frac{1}{2}{/tex} {tex}\times{/tex} 6 {tex}\times{/tex} 3 - {tex}\frac{1}{2}{/tex} {tex}\times{/tex} 3 {tex}\times{/tex} 3 - {tex}\frac{1}{2}{/tex} {tex}\times{/tex}6 {tex}\times{/tex}3
={tex}36 - 9 - 4.5 - 9{/tex}
={tex}13.5\ square\ units{/tex}
Probability that the point will be chosen from the interior of {tex}\triangle{/tex}AJB {tex}= \frac { \text { Area } \Delta J A B } { \text { Area of square } }{/tex} = {tex}\frac{13.5}{36}{/tex} = {tex}\frac{135}{360}{/tex}= {tex}\frac{3}{8}{/tex}.
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