# 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

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

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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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