Question

see attachment :)) I've been stuck on this question forever... I do not understand how they got 2r^2-60r-45=0. I know the formula for the area of the circle is r^2 pi... but still... Can someone answer the question with explanation?

Answer 1

2r² - 60r - 45 = 0

Explanation:

Hang on this is going to be convoluted

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Area of pond

a = πr²

Area of path

a = πr²/10

Combined Area

a = πr² + πr²/10

a = π(r² + r²/10)

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The Combined Area can also be expressed as

a = π(r + 1.5)²

a = π(r² + 3r + 2.25)

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Set the areas equal

π(r² + r²/10) = π(r² + 3r + 2.25)

Divide both sides by π

r² + r²/10 = r² + 3r + 2.25

Subtract r² from both sides

r²/10 = 3r + 2.25

Multiply both sides by 20

2r² = 60r + 45

Subtract 60r + 45 from both sides

2r² - 60r - 45 = 0