rectangle perimeter is 220 meters the area is 2,856 sq meters what are its dimensions dimentions?

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  • 1 decade ago
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    Hi,

    If the perimeter is 220 m, then one length and one width would add to 110 m. Let x = width and 110 - x = length. Then the area would be the length times the width, so 2856 = x(110 - x) or 2856 = 110x - x²

    If the area = -x² + 110x -2856. the maximum area can be found by finding the axis of symmetry for this equation. The equation of the axis is x = -b/(2a) or x = -110/(2*-1) = --110=-2 = 55. So the maximum area would be when each side is 455 meters, giving a square with an area of 3025 m².

    We don't have this area. Instead we have a smaller area of 2856 m². If we set -x² + 110x -2856 = 0 and solve we get x = 42 m or 68 m. so the rectangle with an area of 2856 m² is 42m x 68m.

    I hope this helps!! :-)

  • 1 decade ago

    The perimeter of a rectangle is twice the length plus twice the width. So the length and the width add up to half the perimeter, 110 m in this case. Let the width be w m. Then the length is (110-w) m. So the area is w(110-w).

    So we have 110w - w^2 = 2856

    <=> w^2 - 110w + 2856 = 0

    <=> (w-42) (w-68) = 0

    <=> w = 42 or 68

    and the length is correspondingly 68 or 42.

    So the rectangle has dimensions 68m × 42m.

  • 4 years ago

    Duel equations that the two clean up the given standards. through fact it truly is oblong then it has to have 4 factors with 2 of each and every equivalent to a minimum of one yet another. 2A + 2B = 220 m A + B = a hundred and ten m A * B = 2856 m^2 Use one equation to get one variable equivalent to a quantity and the different variable. So, A = a hundred and ten - B Then replace the A interior the 2d equation with the hot equation. This gets you- (a hundred and ten - B)*B = 2856 110B - B^2 = 2856 So, B^2-a hundred and ten B + 2856 =0 that's a quadratic eqation. any incorrect way would supply you: A = 2856/B then (2856/B) + B = a hundred and ten that's additionally a quadratic. so which you won't be in a position to get around it. Use the quadratic equation and spot in case you get lifelike solutions. you will possibly no longer.

  • 1 decade ago

    rect. perimeter = 2(a+b) = 220

    where a = length and b = breadth

    area= a.b = 2856

    now, 2a+2b=220

    a+b=110

    b=110-a

    put this in area equation

    a(110-a)=2856

    110a-a^2-2856=0

    a^2-110a+2856=0 --- this is a quadratic equation in a.

    the roots are 68 and 42

    thus, the dimensions of the rectangle are 68x42

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  • 1 decade ago

    Not very sure what was your question, but if you are asking what will the length of the sides are, then they will 42m and 68m.

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