Question

If the area of a circle is equal to area of two circles of diameters 10 cm and 24 cm then
find the diameter of the larger circle. ​

Answer 1

Let the radius of the largest circle be R and the small circles be x and y respectively.

x = 10/2 or 5 cm

y = 24/2 or 12 cm

According to the question,

πR² = πx² + πy²

πR² = π ( x² + y² )

cancel π both sides,

R² = x² + y²

R² = (5)² + (12)²

R² = 25 + 144

R² = 169

R = √169

=> R = 13 cm

Answer : 26 cm

Answer 2

The area of circle is :-

$\pi \: r {}^{2}$

Where r is radius.

We know that diameter is twice of the radius.

So,radius of the first and second circle 5cm and 12cm respectively.

Let area of first circle :- x

And, area of second circle :- y

So,

$x = \pi \: 5 { }^{2} \\ = > 25\pi$

$y = \pi \: 12 {}^{2} \\ = > 144\pi$

It is given that the area of larger circle is equal to the area of these circles.

$\pi \: r {}^{2} = 25\pi + 144\pi \\ \pi \: r {}^{2} = 169\pi \\ r {}^{2} = 169 \\ r = 13$

The radius if the larger circle is 13cm.

The diameter of larger circle is :-

$d = 2(r) \\ = > 2(13) \\ = > 26cm$

Therefor the diameter of the larger circle is 26cm

Hope it helped you.