SOLUTION: a pool measuring 12 x 16 meters is surrounded by a path of uniform width. if the are of the pool and the path combined is 480 sq meters what is the width of the path?

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Question 1095561: a pool measuring 12 x 16 meters is surrounded by a path of uniform width. if the are of the pool and the path combined is 480 sq meters what is the width of the path?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
uniform width of the outside path, x
;
12 by 16 assumed as rectangle;

Simplify and solve.

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Let the width of the path =

( can't use )
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The path is 4 m wide
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check:

OK

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
This problem can be easily solved MENTALLY without using equations.

Notice that the difference of dimensions of the pool is 16-12 = 4 meters. If you surround the pool by the path of uniform width, the difference of dimensions of the larger rectangle will be the same 4 meters. Now, you are given that the area of the larger rectangle is 480 square meters. Hence, all you need to do is to find the decomposition of the number 480 into the product of two numbers that differ in 4. What are these numbers ? - But of course, 24 and 20. Then the width of the path is = 4 ft.

Solved.