Math

A rectangle has a width that is 1/8 its length. If the perimeter of the rectangle is 126 inches, what is the width of the rectangle?

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  1. l=8w
    126=2l+2w
    126=2l+2*1/8 l
    126=2l+ l/4 l=2.25 l
    solve for l, then w.

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    bobpursley
  2. You were given:

    A rectangle has a width that is 1/8 its length. If the perimeter of the rectangle is 126 inches, what is the width of the rectangle?

    Length = we don't know and so I'll call it x.

    Width = 1/8(x), which can be written x/8.

    The perimeter given is 126 inches.

    We use the formula for finding the perimeter of a rectangle.

    P = 2L + 2W, where P = perimeter, L = length and W = width.

    Is this clear so far?

    126 inches = 2(x) + 2(x/8)

    I will not use the word inches again for P because you know we are talking about a perimeter of 126 inches, right?

    126 = 2x + x/4

    We now have a fractional equation.

    How do we remove the fraction part?

    We multiply each term by the LCD, which so happens to be 4.

    126(4) = 2x(4) + (x/4)(4)

    504 = 8x + x

    504 = 9x

    To find x, we divide BOTH sides of the equation by 9.

    504 divided by 9 = x

    56 = x

    We are looking for the width, right?

    The width is (1/8)(x), which can also be written x/8.

    We just found x, right?

    To find the width, replace x with 56 in the fraction x/8 and then divide the numerator by the denominator.

    So, x/8 becomes 56/8 = 7

    What is the width of this rectangle?

    Final answer: 7 inches.

    That's it!

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