Area of circular region

[bhumika.k.shah]

OA C

[ajith]

To find out the area of a circle one must know the diameter or radius of that circle. In this case BC is a diameter and BC is also a side of the rectangle ABCD.

BC/AB =3/4 is not alone sufficient to calculate the length of BC
BD = 25 alone is not sufficient to calculate the length of BC
If we combine these two statements,
BD = AB = 25 (parallel sides of a rectangle)
BC = AB*3/4 = 25*3/4

So, C

[vcb]

Agree with the ans..but not the derivation..

BD NOT EQUAL to AB, since BD is the diagonal and AB is a side.

However, AB = CD, hence, BC/CD would also be equal to 3/4. Now that we know the hyp(from stmt 2), and we know the ratio of the sides, we would be able to calculate BC. We can go ahead with C as the ans.

To find out the actual length,
25^2 = BC^2 + CD^2
BC/CD=3/4
CD = (4/3)*BC

so, 25^2 = BC^2 + (4/3)^2*(BC^2)

=> 25^2 = x^2 + (16/9)*x^2 (x=BC) (Dont substitue 25^2 = 625 yet...)
=> 25^2 = (9x^2 + 16x^2)/9
=> (25^2)*9 = 25x^2
=> ((25^2)*9)/25 = x^2
=> 25*9 =x^2
=> 5*3 = x

So BC = 15
thus, radius r = 7.5; area of circle = pi(7.5)^2

Maths is not really my strong subject..I generally make plenty of silly mistakes..any blatant ones here?

[ajith]

Agree with the ans..but not the derivation..

BD NOT EQUAL to AB, since BD is the diagonal and AB is a side.

I agree there and your answer is perfectly Valid


Correcting the mistake
----------------------------------

BC/AB =3/4 is not alone sufficient to calculate the length of BC
BD = 25 alone is not sufficient to calculate the length of BC
If we combine these two statements,
BD =Sqrt( BC^2+ AB^2) =25 (Pythagoras theorem
BC = AB*3/4
BD = Sqrt(AB^2 *9/16 + AB^2) = 25
AB *Sqrt(1+9/16) =25
AB * Sqrt(25/16) =25
AB *5/4 =25
AB = 20
BC = 3AB/4BC = 15

So, C
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[thephoenix]

its c

s1) BC=3/4 AB insuff as it depends on AB

s2) BD=25 insuff as BC can have many diff values

s1)+s2) suff as only one poss value for BC