Question

Two farmers have circular plots. The plots are watered with the same water source placed in the

point common to both the plots as shown in the figure. The sum of their areas is and the

distance between their centres is 14 m.Find the radii of the circles.What value is depicted by the

farmers?





please answer​

Answer 1

Given :-

• Sum of areas of both circular plots = 130π .
• Distance between their centres = 14 m.

To Find :-

• Radii of the circles ?

Solution :-

Let us assume that, radius of bigger plot is R m and radius of smaller plot is r m.

so,

→ R + r = Distance between their centre = 14m. -------- Eqn.(1)

and,

→ πR² + πr² = 130π

→ π(R² + r²) = 130π

→ R² + r² = 130 ------------ Eqn.(2)

now, from Eqn.(1) ,

→ (R + r) = 14

squaring both sides,

→ R² + r² + 2Rr = 196

putting value of Eqn.(2),

→ 130 + 2Rr = 196

→ 2Rr = 196 - 130

→ 2Rr = 66

→ Rr = 33 ----------------- Eqn.(3)

now, we know that,

• (a - b)² = (a + b)² - 4ab.

so, using Eqn.(1) and Eqn.(3) now,

→ (R - r)² = (R+r)² - 4*R*r

→ (R - r)² = (14)² - 4*33

→ (R - r)² = 196 - 132

→ (R - r)² = 64

→ (R - r) = 8 .

adding the result in Eqn.(1) , we get,

→ (R + r) + (R - r) = 14 + 8

→ 2R = 22

→ R = 11 m.

therefore,

→ R + r = 14

→ 11 + r = 14

→ r = 14 - 11

→ r = 3 m.

therefore, the radii of the circles is 11m and 3m.

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