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:

1. Find the highest score.
2. Find the number of centuries scored by him.
3. Find the number of times he scored over 50.
4. Find the number of times he failed to score a 50.

Answer 1

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`.