The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden.

    Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given:
    1. l = 3w + 4 (3 times the width Plus 4 since greater means add)
    2. 2l + 2w = 72
    We substitute equation (1) into equation (2) for l:
    2(3w + 4) + 2w = 72

    Multiply through and simplify:
    6w + 8 + 2w = 72
    (6 +2)w + 8 = 72
    8w + 8 = 72

    To solve this equation for w, we type it in our search engine and we get:
    w = 8

    To solve for l, we substitute w = 8 above into Equation (1):
    l = 3(8) + 4
    l = 24 + 4
    l = 28
     

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