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Activity Discussion Math Mensuration

  • Mensuration

    Posted by Rishi Raj on June 22, 2023 at 3:52 pm

    The length of a rectangle is increased by 34%. By what percentage should the width be reduced to
    keep the area of the rectangle same?

    Akash replied 1 year ago 2 Members · 1 Reply
  • 1 Reply
  • Akash

    Member
    June 22, 2023 at 4:01 pm
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    To solve this problem, let’s assume the original length of the rectangle is L and the original width is W. The original area of the rectangle is given by A = L * W.

    According to the problem, the length is increased by 34%. This means the new length is L + 0.34L = 1.34L.

    Now, we want to find the percentage reduction in the width, which we’ll represent as x%. The new width would then be (1 – x/100)W, since the width is reduced by x%.

    To keep the area of the rectangle the same, the original area (A) should be equal to the new area (A’). So, we have:

    A = A’

    L * W = (1.34L) * ((1 – x/100)W)

    To simplify the equation, we can cancel out the common factors:

    1 * W = 1.34 * (1 – x/100) * W

    Now, we can cancel out the width (W) from both sides:

    1 = 1.34 * (1 – x/100)

    Next, we can simplify the equation further:

    1 = 1.34 – 1.34x/100

    Now, let’s isolate the x term by moving the constants to the other side:

    1.34x/100 = 1.34 – 1

    Simplifying:

    1.34x/100 = 0.34

    Now, we can solve for x by cross-multiplying:

    1.34x = 0.34 * 100

    1.34x = 34

    Dividing both sides by 1.34:

    x = 34/1.34

    x ≈ 25.37

    Therefore, the width should be reduced by approximately 25.37% to keep the area of the rectangle the same when the length is increased by 34%.

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