Question

The diameters of two circular plates are respectively 10 cm and 24 cm. what is the diameter of plate which has area equal to combined area of the two given plates​

Answer 1

Let

Diameter of the 1st circle = 10 cm

Radius 1 = 5 cm

Diameter of the 2nd circle = 24 cm

Radius 2 = 12 cm

Area 1 =

$\pi \: {r1}^{2} \\ = \frac{22}{7} \times 25 \\ = \frac{550}{7} {cm}^{2}$

Area 2 =

$\pi \: {r2}^{2} \\ = \frac{22}{7} \times 144 \\ = \frac{3168}{7} {cm}^{2}$

combined area =

$\frac{550}{7} + \frac{3168}{7} \\ = \frac{3718}{7} {cm}^{2}$

let the radius be r3.

Then

$\pi \: {r3}^{2} = \frac{3718}{7} \\ = \frac{22}{7} {r3}^{2} = \frac{3718}{7} \\ = {r3}^{2} = 169 \\ = r3 = \sqrt{169} = 13$

diameter = 2r

= 2 × 13 = 26 cm

Hope this helps mate