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Question
The runs scored by a cricket player in the last 30 innings are:
75, 125, 36, 89, 154, 56, 12, 28, 96, 142, 78, 54, 30, 88, 116, 104, 55, 84, 10, 29, 31, 08, 24, 136, 117, 22, 99, 80, 112, 35.
Arrange these scores in an ascending order and answer the following:
- Find the highest score.
- Find the number of centuries scored by him.
- Find the number of times he scored over 50.
- Find the number of times he failed to score a 50.
Solution
ar(ΔAPD) = `(sqrt(3)"s"^2)/(4)`
ar(ΔAPD) = `(sqrt(3) xx 8^2)/(4)`
ar(ΔAPD) = `(sqrt(3) xx 64)/(4)`
ar(ΔAPD) = `sqrt(3) xx 16 = 16sqrt(3)"cm"^2`
ar(ΔAPD) = `(1)/(2)` × ar(parallelogram ABCD)
(The area of a triangle is half that of a parallelogram on the same base and between the same parallels)
⇒ ar(parallelogram ABCD) = 2 × ar(ΔAPD)
⇒ ar(parallelogram ABCD) = 2 × `16sqrt(3)"cm"^2`
⇒ ar(parallelogram ABCD) = `32sqrt(3)"cm"^2`.
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