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The length of a rectangular pool is to be 2 times its width, and a sidewalk 6.5 feet wide will surround the pool. If a total area of 1809 ft2 has been set aside for construction, what are the dimensions of the pool?
- PinkgreenLv 71 month ago
Let w ft be the width of the pool, then 2w
will be the length. 1809 ft^2 is the total area
of the pool & the sidewalk, you should first
write down the true length & width of the
rectangle for this area which are
& then write down an equation & solve for w
& hence get the dimensions of the pool.
Ans. w=20.5 ft; 2w=41 ft.
- KrishnamurthyLv 71 month ago
The length of a rectangular pool is to be 2 times its width,
and a sidewalk 6.5 feet wide will surround the pool.
If a total area of 1809 ft^2 has been set aside for construction,
what are the dimensions of the pool?
(2w + 13)*(w + 13) = 1809
w = 41/2, l = 41
The length of the pool is 41 feet and its width is 20 1/2 feet.
- Blue JackLv 61 month ago
A = 1809 ft²
s = 6.5 ft
l = pool length
w = pool width
l = 2w
A = (2w + 2s)(w + 2s)
1809 = (2w + 2(6.5))(w + 2(6.5)
1809 = 2w² + 13w + 26w + 13²
2w² + 39w - 1640 = 0
If ax² + bx + c = 0 then x = [-b ± √(b² - 4ac)] / 2a
w = [-39 ± √(39² - 4(2)(-1640))] / 2(2)
w = -39/4 ± 121/4
w = 20.5, -40
Throw out the negative value which makes no sense.
w = 20.5 ft
l = 2w
l = 2(20.5)
l = 41 ft
- PuzzlingLv 71 month ago
Let w be the width.
Let 2w be the length.
The total width of the area is w + 2(6.5) --> w + 13
The total length of the area is 2w + 2(6.5) --> 2w + 13
The total area is 1809 ft²:
(w + 13)(2w + 13) = 1809
Expand the left side:
2w² + 13w + 26w + 169 = 1809
2w² + 39w - 1640 = 0
(2w - 41)(w + 40) = 0
That leads to two potential solutions:
2w - 41 = 0
2w = 41
w = 20.5
w + 40 = 0
w = -40
We can ignore the negative result.
Calculate the length (double the width):
2w = 2(20.5) = 41
The pool is 20.5 feet wide and 41 feet long.
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- Daniel HLv 51 month ago
width = w
length = 2w
entier = pool plus border sidwalk
width = w + 2(6.5ft) = w + 13ft
length = 2w + 2(6.5ft) = 2w + 13ft
Area = 1809ft^2
1809ft^2 = (w + 13ft)(2w + 13ft)
1809ft^2 = 2w^2 + 39ftw + 169ft^2
2w^2 + 39ftw - 1640ft
w = 20.5ft and/or -40ft
ignore negative width
w = 20.5ft
l = 41ft
(41 + 13)(20.5 + 13) = 1809ft
- 1 month ago
Let's say the dimensions of the pool are l and w. imagine a "frame" of 6.5 ft added around the pool. the dimensions of the new rectangle are l + 6.5 + 6.5 (6.5 on each side) and w + 6.5 + 6.5 or in short l + 13 and w + 13. We know the total surface is 1809, so (l + 13)(w + 13) = 1809.
We also know that the length is twice the width, so we could say l = 2w. This means (2w + 13)(w + 13) = 1809. or 2w² + 39w + 169 = 1809 or 2w² + 39w - 1640 = 0.
Solve this equation and you'll find your dimensions.