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the length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?

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  1. 5 July, 11:11
    0
    The rectangle is 13cm by 11cm (or 11cm by 13cm)

    Step-by-step explanation:

    Length plus width = 25

    L+W = 24

    Area is 143

    A = LW

    143 = LW

    We have two equations and two unknowns

    L+W = 24 Solve for W by subtracting L from each side W = 24-L

    143 = LW

    Now substitute into the second equation

    143 = L (24-L)

    Distribute

    143 = 24L - L^2

    Multiply by - 1

    -143 = - 24L + L^2

    -143 = L^2 - 24L

    Completing the square

    -24/2 = - 12 - 12^2 = 144

    Add 144 to each side

    -143+144 = L^2 - 24L+144

    1 = (L-12) ^2

    Take the square root of each side

    ±sqrt (1) = sqrt ((L-12) ^2)

    ±sqrt (1) = (L-12)

    Add 12 to each side

    12±sqrt (1) = (L-12) + 12

    12±1 = L

    13=L or 11=L

    Now we need to find W

    W = 24 - L

    W = 24-13 W = 24-11

    W = 11 or W = 13
  2. 5 July, 11:32
    0
    L=13, w=11
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