SOLUTION: Suppose the area of the swimming pool is doubled, would its length and width also doubled? Justify your answer. The length is 35 and the width is 16
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Question 1197300: Suppose the area of the swimming pool is doubled, would its length and width also doubled? Justify your answer. The length is 35 and the width is 16 Found 2 solutions by math_helper, Theo:Answer by math_helper(2461) (Show Source):
Clearly, no.
If A = L*W then if you double L and double W, you get:
(2L)*(2W) = 4(L*W) = 4*A (i.e. four times the original area).
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If the new swimming pool shape is similar to the old one, then L and W can be scaled by to achieve a doubling of the area: * = =
You can put this solution on YOUR website! area = length * width
multiply both sides of the equation by 2 to get:
2 * area = 2 * length * width
2 * length * width = 2 * width * length = (2 * length) * width or (2 * width) * length.
what this suggests is that either the length is multiplied by 2 or the width is multiplied by 2, but not both.
if the length is 35 and the width is 16, then the area is equal to 35 * 16 = 560.
2 time the area = 2 * 560 = 1120.
(2 * width) * length = 35 * 32 = 1120.
either the length is doubled or the width is doubled, but not both.
if both are affected equally, then both the length and the width are multiplied by sqrt(2).
35 * sqrt(2) * 16 * sqrt(2) = 35 * 16 * sqrt(2)^2 = 35 * 16 * 2.
either way, the length and the width are not doubled if the area is doubled.
