SOLUTION: A piece of wire is shaped to enclose an equilateral triangle whose area is (16 (sqrt 3) ) cm^2. It is then reshaped to enclose a rectangle whose length is 9 cm. Find the area of th

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Question 234893: A piece of wire is shaped to enclose an equilateral triangle whose area is (16 (sqrt 3) ) cm^2. It is then reshaped to enclose a rectangle whose length is 9 cm. Find the area of the rectangle.
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Answer by solver91311(24713) About Me  (Show Source):
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The area of an equilateral triangle given the measure of one side, , is:

.

Therefore:







Therefore the perimeter of the triangle, and the length of the wire is 24.

The perimeter of a rectangle is:



So:



So the width is



If the length is 9 and the width is 3, the area must be 27.


John