Comparing Areas ( 2 )

Geometry Level 2

Examine the figure and compare the Red and the Blue areas?

B = 2 R B = 2 R R = 1.5 B R = 1.5 B B = R B = R R = 2 B R = 2 B B = 1.5 R B = 1.5 R

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2 solutions

Hana Wehbi
May 28, 2020

Area of Blue is : \text \color{#3D99F6}{{Area of Blue is :}} 10 π 2 Area of White 10\pi^2 - \text{ Area of White }

Area of Red Is : \text\color{#D61F06}{ {Area of Red Is }:} ( 6 π 2 + 4 π 2 ) Area of White (6\pi^2 + 4\pi^2 ) - \text { Area of White }

Thus, Red = Blue \text { Thus, \color{#D61F06}Red = \color{#3D99F6}Blue }

Aryan Sanghi
May 28, 2020

Considering area of circle of radius 10

A 1 = B + W 1 + W 2 A_1 = B + W_1 + W_2

π ( 10 ) 2 = B + W 1 + W 2 π(10)^2 = B + W_1 + W_2


Considering area of circle of radius 6

A 2 = R 2 + W 2 A_2 = R_2 + W_2

π ( 6 ) 2 = R 2 + W 2 π(6)^2 = R_2 + W_2


Considering area of circle of radius 8

A 3 = R 1 + W 1 A_3 = R_1 + W_1

π ( 8 ) 2 = R 1 + W 1 π(8)^2 = R_1 + W_1


Now,

6 2 + 8 2 = 1 0 2 6^2 + 8^2 = 10^2

π ( 6 ) 2 + π ( 8 ) 2 = π ( 10 ) 2 π(6)^2 + π(8)^2 = π(10)^2

( R 2 + W 2 ) + ( R 1 + W 1 ) = B + W 1 + W 2 (R_2 + W_2) + (R_1 + W_1) = B + W_1 + W_2

R 1 + R 2 = B R_1 + R_2 = B

As R 1 + R 2 = R R_1 + R_2 = R

Therefore, R = B \boxed{R = B}

Thank you, Nice solution

Hana Wehbi - 1 year ago

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You're welcome mam.

Aryan Sanghi - 1 year ago

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