Question

b. Find the perimeter of a circle whose area is equal to the sum of the areas of [
the circles with diameters 10 cm and 24 cm. ANSWER FAST​

Answer 1

Answer: Diameter = 2× radius = 2× 25 = 50 cm

Step-by-step explanation:

We have the formula for area of circle,

Area=π r  

2

, where r is the radius of the circle

Let, the circle whose area is equal to the sum of the areas of the two circles of radii 24 cm  and 7 cm be A  

3

​  and its radius be r  

3

​  

Area of circle with radius,r  

1

​  

=24 cm be A  

1

​  

 

Area of circle with radius,r  

2

​  

=7 cm be A  

2

​  

 

Given,

A  

3

​  

=A  

1

​  

+A  

2

​  

 

π(r  

3

​  

)  

2

=π(r  

1

​  

)  

2

+π(r  

2

​  

)  

2

 

π(r  

3

​  

)  

2

=π[(r  

1

​  

)  

2

+(r  

2

​  

)  

2

]

(r  

3

​  

)  

2

=(r  

1

​  

)  

2

+(r  

2

​  

)  

2

 

(r  

3

​  

)  

2

=(24)  

2

+(7)  

2

=625=25  

2

 

r  

3

​  

=25

Diameter = 2× radius = 2× 25 = 50 cm