5. A 50-inch piece of wire is bent into the shape of a rectangle. Find the dimensions of the rectangle of maximum area that can be for

Question

5. A 50-inch piece of wire is bent into the shape of a rectangle. Find the dimensions of the rectangle
of maximum area that can be formed from the wire,

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Thiên Ân 5 months 2021-08-16T17:17:59+00:00 1 Answers 6 views 0

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    2021-08-16T17:19:26+00:00

    Answer:

    length = 12.5 in, width = 12.5 in, Area = 156.25 in²

    Step-by-step explanation:

    To get the maximum area, the wire can be shaped into a square. We can say that the length and width of the rectangle must be equal to each other, and call this value “x”.

    Therefore, we can write an equation for the perimeter:

    • 2x + 2x = 50
    • 4x = 50
    • x = 12.5

    The area of the rectangle is calculated using the formula:

    • A = lw

    Or in our case, the area of the rectangle is the area of a square:

    • A = x²

    Substitute x = 12.5 into this equation.

    • A = (12.5)²
    • A = 156.25

    The maximum area that can be formed from the wire is 156.25 in², and the dimensions of the rectangle are 12.5 x 12.5 in.

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