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8_murik_8 [283]

2 years ago

15

A 2 feet piece of wire is cut into two pieces and once a piece is bent into a square and the other is bent into an equilateral t

riangle. Where should the wire cut so that the total enclosed area by both shapes is at the maximum?

1 answer:

SpyIntel [72]2 years ago

3 0

Answer:

Explanation:

Let x ft be used to make square and 2-x ft be used to make equilateral triangle.

each side of square = x/4

area of square = ( x /4 )²

Each side of triangle

= (2-x) /3

Area of triangle = 1/2 (2-x)²/9 sin 60

= √3 / 36 x (2-x)²

Total area

A = ( x /4 )² +√3 / 36 (2-x)²

For maximum area

dA/dx = 0

1/16( 2x ) -√3 / 36 x2(2-x) = 0

x / 8 - √3(2-x)/ 18 = 0

x / 8 - √3/9 + √3/18 x = 0

x ( 1/8 + √3/18 ) = √3/9

x(.125 +.096 ) = .192

x = .868 ft

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Answer:

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Solution:

As per the question:

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Using binomial theorem in the above eqn:

We know that:

$(1 + x)^{a} = 1 + ax$

Thus eqn (1) becomes:

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Answer:

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Explanation:

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