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MathematicsMathematics
15 May, 14:32

A cabinet door has a perimeter of 62 inches its area is 228 in.² what are the dimensions of the door

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Answers (1)
  1. 15 May, 14:57
    0
    P=2 (L+W)

    A=LW

    given

    P=62

    62=2 (L+W)

    divide 2

    31=L+W

    minus W

    L=31-W

    sub into other one

    A=LW

    A = (31-W) (W)

    228=31W-W^2

    times - 1

    W^2-31W=-228

    add 228 both sides

    W^2-31W+228=0

    factor

    what 2 numbers multiply to get 228 and add to get - 31

    -19 and - 12

    (W-19) (W-12) = 0

    set to zero

    W-19=0

    W=19

    W-12=0

    W=12

    sub back

    L=31-W

    L=31-12

    L=19

    or

    L=31-19

    L=12

    the doorway is 12in by 19in
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