Andy C. answered • 06/06/18

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Perimeter = 2L + 2w

46 = 2L + 2w

46 = 2(L+w)

23 = L+w

The dimensions of the pool are x and 23-x <--- answer to part 1

The path adds 2(x-8)= 2x-16 meters to each dimension.

The dimensions of the pool and walkway are 2x-16+x = 3x-16 and 2x-16 + 23-x = x + 7

The entire area is then (3x-16)(x+7)

The area of the pool is x(23-x)

Entire Area = Area of pool + area of walkway

(3x-16)(x+7) = x(23-x) + 140

3x^2 + 21x - 16x - 112 = 23x - x^2 + 140

3x^2 + 5x - 112 = 23x - x^2 + 140

4x^2 -18x - 252 = 0

2x^2 - 9x - 126 = 0

x = [ 9 +or- sqrt( 81 + 4(2)(126))]/4

= [ 9 +or- sqrt( 81 + 1008)]/4

= [ 9 +or- sqrt(1089)]/4

= [ 9 +or- 33]/4

the negative case results in negative measures

x = (9+33)/4 = 42/4 = 21/2 = 10.5

**The dimensions of the pool 10.5 and 23-10.5 = 12.5**

**The width of the path is 10.5-8 = 2.5**

CHECK:

The dimensions of the entire area is (10.5 + 2*2.5) = 10.5 +5 = 15.5 and 12.5 + 2*2.5 = 12.5 + 5 = 17.5

The entire area is 15.5 * 17.5 = 271.25

The area of the pool is 10.5 * 12.5 = 131.25

271.25-131.25 = 140

The results above in bold are correct!