Question
A 6 m by 9 m swimming pool is surrounded by a deck which has a constant width. How wide is the deck if its area equals the area of the pool?
I got 6*9=54 so for the deck xy=54 but I don't know where to go.
I got 6*9=54 so for the deck xy=54 but I don't know where to go.
Answers
Damon
pool area = 54
whole thing
L = 9+2s
w = 6+2s
area of whole thing = (9+2s)(6+2s)
so
(9+2s)(6+2s) = 2 * 54 = 108
54 + 30 s + 4 s^2 - 108 = 0
4 s^2 + 30 s - 54 = 0
2 s^2 + 15 s - 27 = 0
(2s-3)(s+9) = 0
s = 3/2 = 1.5
whole thing
L = 9+2s
w = 6+2s
area of whole thing = (9+2s)(6+2s)
so
(9+2s)(6+2s) = 2 * 54 = 108
54 + 30 s + 4 s^2 - 108 = 0
4 s^2 + 30 s - 54 = 0
2 s^2 + 15 s - 27 = 0
(2s-3)(s+9) = 0
s = 3/2 = 1.5