In the figure, ABCD is a rectangle and PBCQ is a square. The probability of marking adot, without looking to be within the square is
(a) What is the probability of the dot to be
within the rectangle APQD ?
(b) If the area of the square is
8 square centimetres, what is the area
of the rectangle ABCD ?
(c) If the area of the square is b and if the probability of the dot being in the square is
them what is the area of the rectangle APQD ?
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Answer:
Wehave to find the ratio of AE:AD i.e. tan x =
AD
AE
(let ∠ODC=∠ADE=x)
Let r be the radius of the circle
and, Let l and b be the length and breadth of the rectangle.
Then, by Pythagoras theorem in △ABD
l
2
+b
2
=(2r)
2
l
2
+b
2
=4r
2
(1)
Now, acc to question: Area of circle:area of rectangle =π:
3
⇒
lb
πr
2
=
3
π
⇒lb=
3
r
2
(2)
Dividing (1) by (2) we get,
lb
l
2
+
lb
b
2
=
3
r
2
4r
2
⇒
b
l
+
l
b
=
3
4
b
l
=
3
⇒
l
b
=
3
1
Now,
AD
AE
=tanx=
3
1
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