Question

The sum of diameters of two circles is 14 cm and the difference of their circumferences
is 8 cm. Find the circumferences of the two circles.
without using any fomrula​

Answer 1

$\rm\underline\bold{Question \purple{\huge{\checkmark}}}$

The sum of diameters of two circles is 14 cm and the difference of their circumferences

is 8 cm. Find the circumferences of the two circles.

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Answer 2

Answer:

difference of circumferences is 8cm

∏x - ∏y = 8

∏(x-y) = 8

x - y = 8/∏

 

We have two equations:

x + y = 14

x - y = 8/∏     add equations

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2x = 14 + 8/∏

x = (14+8/∏)/2

x = 7 + 4/∏

 

Replace x with 7+4/∏ in one of the original equations

 

x + y = 14

7+4/∏ + y = 14

y = 14 - 7 - 4/∏

y = 7 - 4/∏

 

Diameter of circle 1:  7 + 4/∏

Circumference of circle 1

∏(7+4/∏) = 7∏ + 4

 

Diameter of circle 2: 7 - 4/∏

Circumference of circle 2:

∏(7-4/∏) = 7∏-4