SOLUTION: i don't understand how to do this can you please help me? its a worksheet the problem is: a rectangular swimming pool is 10 m longer than it is wide. a walkway 2 m wide surround

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i don't understand how to do this can you please help me? its a worksheet the problem is: a rectangular swimming pool is 10 m longer than it is wide. a walkway 2 m wide surround      Log On


   



Question 179490: i don't understand how to do this can you please help me? its a worksheet
the problem is:
a rectangular swimming pool is 10 m longer than it is wide. a walkway 2 m wide surrounds the pool. find the dimensions of the pool if the area of the walkway is 216 m squared.

Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a rectangular swimming pool is 10 m longer than it is wide. a walkway 2 m wide surrounds the pool. find the dimensions of the pool if the area of the walkway is 216 m squared.
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The area of the pool is l*w, length times width
The area enclosed by the walkway, including the pool, is (l+2)*(w+2).
The area of the walkway is (l+2)*(w+2) - l*w.
(l+2)*(w+2) - l*w = 216
lw + 2l + 2w + 4 - lw = 216
2l + 2w + 4 = 216
l + w = 106 (a rectangular swimming pool is 10 m longer than it is wide)
l = w+10
w+10 + w = 106
2w = 96
w = 48 meters
l = 58 meters

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the area of the pool A%5Bp%5D
Call the area of the walkway A%5Bw%5D
Call the total area A%5Bt%5D
Call the width of the pool wm.
The length of the pool is w+%2B+10m
To find the area of the walkway plus the pool,
I must add 2m to both dimensions of the pool
A%5Bp%5D+=+w%2A%28w+%2B+10%29m2
A%5Bt%5D+=+%28w+%2B+2%29%2A%28w+%2B+10+%2B+2%29
A%5Bt%5D+=+%28w+%2B+2%29%2A%28w+%2B+12%29
A%5Bt%5D+=+w%5E2+%2B+2w+%2B+12w+%2B+24
A%5Bt%5D+=+w%5E2+%2B+14w+%2B+24m2
A%5Bt%5D+=+A%5Bp%5D+%2B+A%5Bw%5D
A%5Bw%5D+=+216m2
A%5Bt%5D+=+A%5Bp%5D+%2B+216m2
A%5Bp%5D+%2B+216+=+w%5E2+%2B+14w+%2B+24m2
A%5Bp%5D+=+w%5E2+%2B+14w+-+192m2
and also given is
A%5Bp%5D+=+w%2A%28w+%2B+10%29m2
A%5Bp%5D+=+w%5E2+%2B+10wm2
I can set them equal to eachother
w%5E2+%2B+10w+=+w%5E2+%2B+14w+-+192
-4w+=+-192
w+=+48
and, since the length is w+%2B+10m
w+%2B+10+=+58
The dimesions of the pool are 48m x 58m
check:
A%5Bp%5D+=+48%2A58m2
A%5Bp%5D+=+2784m2
A%5Bt%5D+=+2784+%2B+216
A%5Bt%5D+=+3000
A%5Bt%5D+=+w%5E2+%2B+14w+%2B+24m2
3000+=+48%5E2+%2B+14%2A48+%2B+24m2
3000+=+2304+%2B+672+%2B+24
3000+=+3000
OK