if the length of a certain rectangle is decreased by 4cm and the width is increased by 3cm,a square with the same area would result.find the

Question

if the length of a certain rectangle is decreased by 4cm and the width is increased by 3cm,a square with the same area would result.find the perimeter of original rectangle
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Hồng Cúc 3 years 2021-08-31T05:45:59+00:00 1 Answers 6 views 0

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  1. Dau
    0
    2021-08-31T05:47:19+00:00
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    Answer:

    The perimeter is 50

    Step-by-step explanation:

    The original area is LW

    The new area is (L-4)(W+3)

    These areas are the same

    1:      (L-4)(W+3)=LW

    You are also told that the new figure is a square, hence

    2:     (L-4)=(W+3)

    Equation (2) implies

    3:     L=W+7

    Substitute for L in Equation (1) and solve for W

    (W+7-4)(W+3)=(W+7)W

    W^2+3W+7W+21-4W-12=W^2+7W

    6W+9=7W

    W=9

    Now use Equation (3) to solve for L

    L=16

    The perimeter is 2W+2L

    P=18+32=50

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