Question

I have a geometry question ... its simple but quite irritating ..... am unable to solve it

the perimeter of a circle is 18 times more then the area of right angled triangle .the radius is 2 times height of the triangle and base is 6 times more then the radius of the circle. calculate the area of the circle. answer option : 88 , 616, 308,176, 693 -- one of the answer is correct

Answer 1

Can we agree on these equations:
\[2\pi r=18(\frac{1}{2}bh)=9bh\]
\[r=2h, h=\frac{r}{2}\]
\[b=r+6\]
So
\[2\pi r=9(r+6)(\frac{r}{2})\]

Answer 2

Where am I going wrong?

Answer 3

Oh I see. I didn't read carefully the base is 6r

Answer 4

fix typos
There are a lot of facts to write down:
p= 2 pi r
p= 18 A
A = 0.5 b h
b= 6r
r= 2h

and we want to find pi r^2

Answer 5

So\[2\pi r=9(6r)(\frac{r}{2})\]

Answer 6

Which produces a radius of

Answer 7

\[r=\frac{2\pi}{27}\]

Answer 8

And an area of something that is way too small.

Answer 9

which does not give us anything like the choices provided

Answer 10

Exactly. So either I made a calculation error or we are misinterpreting the problem.

Answer 11

No, I got the same thing.
Maybe the problem is interpreting
base is 6 times more then the radius

Answer 12

Or the perimeter is 18 times more than the area of the triangle.

Answer 13

reverse engineer the problem, to find what the base should be?

Answer 14

6 times more than the radius implies we should add something to the radius to get the base but what???

Answer 15

ashish should get some details from his teacher about this one.

Answer 16

I agree. I have wasted quite enough time on it.