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30 May, 12:06

the length of a rectangle is 3cm more than the width. find the length and the width if the perimeter of the rectangle is 98cm.

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  1. 30 May, 15:18
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    The perimeter of a rectangle is length + length + width + width.

    We know that the length of a rectangle is 3cm more than its width, which gives us the equation: (l for length and w for width)

    l = 3 + w

    We also know that the perimeter of the rectangle is 98cm, which gives us the equation:

    98 = 2l + 2w (equation for perimeter of a rectangle as noted above)

    We can divide both sides of this equation by 2 to get:

    49 = l + w

    Now we'll stick l = 3 + w into the above equation, which gives us:

    49 = 3 + w + w

    which simplifies to 49 = 3 + 2w.

    Now we'll subtract 3 from both sides:

    49 - 3 = 46

    3 + 2w - 3 = 2w

    which gives us 46 = 2w.

    Dividing both sides by 2 gives us 23 = w.

    Substituting w = 23 into the equation l = 3 + w gives us:

    l = 3 + 23

    l = 26cm.

    Let's check our answer. 26cm is 3cm more than 23cm. 26cm + 26cm + 23cm + 23cm gives us 98cm. The length is 26cm and the width is 23cm.
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