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
Algebra.Com
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.
>>Please show your solution. Thanks
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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:
\ +\ 2w\ = 24)
So the width is
If the length is 9 and the width is 3, the area must be 27.
John
RELATED QUESTIONS
A piece of wire is shaped to enclose an equilateral triangle whose area is 27.71cm^2. It... (answered by rothauserc,Theo)
A piece of wire is shaped to enclose a rectangle with a length of 15cm and whose area is... (answered by ikleyn)
A piece of wire is shaped to enclose a square with an area of 121 in^2. It is reshaped to (answered by shweta)
a piece of wire is shaped to enclose a square, whose area is 121sq. in. it is then... (answered by ptaylor)
Please help me with my Geometry assignment.
here's the problem.
A piece of wire is... (answered by stanbon)
A piece of wire is in the shape of an equilateral triangle with side 80 cm. The wire is... (answered by ankor@dixie-net.com)
A wire is bent into a square enclosing an Area of 48cm^2. If it is to be reshaped as an... (answered by josgarithmetic)
What is the side lengths of an equilateral triangle, whose area is 16 sqrt(3)cm^2... (answered by KMST)
Find the perimeter of an equilateral triangle whose area is equal to that of a triangle... (answered by math_tutor2020)