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7 July, 00:40

The length of a rectangle is 7cm less than twice it's width. If the area is 30 sq. cm, find the dimensions

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  1. 7 July, 00:49
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    The rectangle is 6 centimeters by 5 centimeters.
  2. 7 July, 01:00
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    If the width of a rectangle is 7 centimeters less than twice its length and its area is 30 square centimeters, then the dimensions of the rectangle are 6 centimeters by 5 centimeters.

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    To find the dimensions of the rectangle, we can set up a system of equations and use substitution to solve it. We are given that the width, call it w, of the rectangle is 7 centimeters less than twice its length, call it l. This gives the following equation:

    w = 2l - 7

    We are also given that the area is 30 square centimeters. The area of a rectangle, call it A, can be found using the formula A = l*w, or area equals the rectangle's length times its width. Therefore, we have another equation as follows:

    30 = l*w

    Now that we have two equations in l and w, we can use substitution to solve. To do this, we first plug w = 2l - 7 into 30 = lw.

    30 = l (2l - 7) = 2l2 - 7l

    Now, we can solve the equation 30 = 2l2 - 7l to find our length.

    30 = 2l2 - 7l

    Subtract 30 from both sides and interchange sides.

    2l2 - 7l - 30 = 0

    Factor the left-hand side.

    (2l + 5) (l - 6) = 0

    Set each factor equal to 0 and solve.

    2l + 5 = 0 or l - 6 = 0

    2l = - 5 or l = 6

    l = - 5/2 or l = 6

    We get that the length is 6 or - 5/2. Since we can't have a negative length, the length is 6 centimeters. Now we plug l = 6 into either one of the original equations to solve for w and find our width.

    30 = 6w

    5 = w

    or

    w = 2 (6) - 7

    w = 5

    In both cases we get that the width is 5 centimeters, so we have that the dimensions of the rectangle are 6 centimeters by 5 centimeters.
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