maths

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the length of a rectangle is 3 less than 5 times its width.
Write a simpified algebriac expression for the perimeter of a rectangle.
If the rectangle width is tripled and its length is doubled,the perimeter of new rectangle is 92cm greater than the original perimeter.
Find the area of the original rectangle.

  • maths -

    original width ---> x
    original width ---> 5x-3

    Perimeter = 2x +2(5x-3) = ....

    new width --->3x
    new length ---> 2(5x-3)

    so 2(3x) + 2(5x-3) = 92
    solve for x
    ....

    then evaluate x(5x-3)

    let me know what you get.

  • maths -

    Hi aisha,

    Let's start with formulating an algebriac expression for the perimeter.
    We know that perimeter of rectangle = 2(length) + 2(width).

    Since we don't know length or width, we let x be the width of the rectangle.
    Hence length = 5x-3 [because length = (5 X width) - 3].
    So perimeter = 2[5x-3]+2(x) = 10x-6+2x= 12x-6. That answers the first part.

    If width is tripled, new width = 3x.
    If length is doubled, new length = 2(5x-
    3) = 10x-6. So new perimeter = 2(3x)+2(10x-6) = 6x+20x-12= 26x-12.

    Now, perimeter of new rectangle - perimeter of original rectangle = 92cm.
    So [26x-12]-[12x-6] = 92cm
    Simplifying the left hand side, 14x-6=92cm
    Therefore, 24x=98cm, x=98/14=7cm.

    So to find area of original rectangle, it is length X width = (5x-3)(x) = 5x^2 - 3x = 5(7X7) - 3(7) = 224cm^2
    Hope I helped! (:

    -J

  • maths -

    Go with J's solution, I noticed an error near the end of mine,
    my equation should have been
    2(3x) + 4(5x-3) = 92

  • maths -

    Oops sorry! I realised that I also made a mistake near the end.
    When I said "...Therefore, 24x=98cm.." I meant 14x (Not 24!) = 98cm. =)

  • maths -

    The length of a rectangle is 3cm less than twice the width.The perimeter of the rectangles of the sides of the rectangle is 24cm.Find the lengths of the sides of the rectangle.

  • maths,algebra -

    In a given rectangle,the length is two less than four times the width,w.Find the expression that represents the area and the perimeter.

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