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.
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
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
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
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
To find the formula for the walkway, we can think of the pool and the walkway as two separate rectangles.
The length of the outer rectangle (including the walkway) is (x+2) meters, because there is a 1m walkway on each side of the pool. Similarly, the width of the outer rectangle is (x-5+2) = (x-3) meters.
Therefore, the area of the outer rectangle is (x+2)(x-3).
Now, we know that the area of the inner rectangle (just the pool) is x(x-5), and the area of the outer rectangle (including the walkway) is (x+2)(x-3).
We also know that the increase in area due to the walkway is 36 m^2. So we can set up an equation:
(x+2)(x-3) - x(x-5) = 36
Expanding and simplifying this equation, we get:
(x^2 - 3x + 2x - 6) - (x^2 - 5x) = 36
After cancelling out the common terms, the equation becomes:
x - 6 = 36
Solving for x, we find:
x = 42
So the length of the pool is 42 meters, and the width of the pool is 42 - 5 = 37 meters.