Algebra

A rectangular pool was 5 m longer than it was wide. When a brick walkway 1m wide was added around the pool, the area was increased by 36 m^2. Find the dimension of pool itself.

Dimension of pool:
Length= x
Width= x-5

So I know the area= x(x-5) = x^2-5l

And I also so know, when the area was increased the new formula would be x^2-5x+36

I just don't know how to find the formula for the walkway.

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  1. Total Area - walkway area = pool area

    walkway area is LxW ... but you add 1 on to each side of the pool : )
    = (x+5 + 1 + 1)(x + 1 + 1)
    = (x +7)(x + 2)

    Your pool area was correct at x^2 -5x

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  2. new length = x+2 , think of it as 1+x+1
    new width = x-5 + 2 = x-3
    new area = (x+2)(x-3) = x^2 - x - 6

    x^2 - x - 6 - (x^2 + 5x) = 36
    x^2 - x - 6 -x^2 - 5x = 36
    -6x = 42
    x = -7 , makes no sense

    or, your way
    (x+2)(x-3) = x^2 + 5x + 36
    x^2 - x - 6 = x^2 + 5x + 36
    -6x = 42
    same silly result

    your question is bogus

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  3. the walkway added 2 m to both the length and width of the pool area (1 m all around)

    (x + 2) (x - 3) = x^2 - 5x + 36

    x^2 - x - 6 = x^2 - 5x + 36

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  4. This is the second error I made today, need more coffee.

    pick it up from :
    x^2 - x - 6 - (x^2 + 5x) = 36 <--- I copied it as x^2 + 5x instead of x^2 - 5x
    x^2 - x - 6 - (x^2 - 5x) = 36
    x^2 - x - 6 -x^2 + 5x = 36
    4x = 42
    x = 10.5
    pool is 10.5 m by 5.5 m

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