Question

If the sum of areas of two circles, is equal to the area of the third circle, which of these could be the ratio of the diameter of circles?
60:21:61,
17:12:31 ,
12:35:37,
23:36:45​

Answer 1

Answer:

The correct option is (c) $12:35:37$

Step-by-step explanation:

Assume A:B:C is $12:35:37$

We are aware that diameter is twice as large as radius.

Diameter of A is $12.$

Then radius of A is $12/2=6$

Diameter of B is 35.

Then radius of B is $35/2$

Diameter of C is $37.$

Then radius of C is $37/2$

The area of a circle is equal to $\pi r^{2}$

Therefore, according to the given condition

On Solving we get,

$\pi r^{2}+\pi r^{2} =\pi r^{2}$

$\pi 6^{2}+\pi (\frac{35}{2})^{2} =\pi (\frac{37}{2} )^{2}$

$\pi[ 6^{2}+(\frac{35}{2})^{2}] =\pi (\frac{37}{2} )^{2}$

$\pi[ 36+\frac{1225}{4} ] =\pi (\frac{37}{2} )^{2}$

$\pi[ \frac{1369}{4}] =\pi (\frac{37}{2} )^{2}$

$\pi (\frac{37}{2} )^{2}= \pi (\frac{37}{2} )^{2}$

Therefore, option (c) is correct.

#SPJ3