SOLUTION: A piece of wire is shaped to enclose an equilateral triangle whose area is 27.71cm^2. It is then reshaped to enclose a rectangle whose length is 9cm., find the area of the rectangl
Algebra.Com
Question 1124653: A piece of wire is shaped to enclose an equilateral triangle whose area is 27.71cm^2. It is then reshaped to enclose a rectangle whose length is 9cm., find the area of the rectangle
Found 2 solutions by rothauserc, Theo:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let s be the length of a side of the equilateral triangle
:
area of equilateral triangle in terms of s is
:
Area = s^2 * square root(3)/4
:
Note this formula comes from the fact that the base is s/2 and height = s * square root(3)/2 for an equilateral triangle
:
27.71 = s^2 * square root(3)/4
:
s^2 = (4 * 27.27)/square root(3) = 62.9774
:
s = square root(62.9774) is approximately 7.94 cm
:
Perimeter of the equilateral triangle is 3 * 7.94 = 23.82 cm
:
Perimeter of rectangle is 2l + 2w where l is length and w is width
:
we are given that l=9
:
2(9) +2w = 23.82
:
2w = 23.82 -18 = 5.82
:
w = 2.91 cm
:
Area of rectangle(A) = l * w
:
*************************
A = 9 * 2.91 = 26.19 cm^2
*************************
:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the area of the equilateral triangle is 27.71 square centimeters.
the formula for the area of an equilateral triangle is A = sqrt(3) / 4 * S^2, where S is the side of the equilateral triangle.
this formula becomes 27.71 = sqrt(3) / 4 * S^2
solve for S to get S = sqrt(27.71 * 4 / sqrt(3)) = 7.99959398.
that's the length of one side of the triangle.
the perimeter of the triangle is 3 times that = 23.99878194.
that's the length of the wire that was used to shape the triangle.
the length of the rectangle is 9.
the formula for the perimeter of the rectangle is 2 * (L + W) = 23.99878194.
divide both sides of that equation by 2 to get L + W = 23.99878194 / 2 = 11.99939097.
since L = 9, W must be equal to 11.99939097 minus 9 = 2.999390969.
you have:
L = 9
W = 2.999390969
the area of the rectangle is equal to L * W = 9 * 2.999390969 = 26.99451872 square centimeters.
RELATED QUESTIONS
A piece of wire is shaped to enclose an equilateral triangle whose area is (16 (sqrt 3) ) (answered by solver91311)
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)
A piece of wire is shaped to enclose a rectangle with a length of 15cm and whose area is... (answered by ikleyn)
Please help me with my Geometry assignment.
here's the problem.
A piece of wire is... (answered by stanbon)
A wire is bent into a square enclosing an Area of 48cm^2. If it is to be reshaped as an... (answered by josgarithmetic)
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 farmer has 3000 feet of wire to enclose a rectangular field. He plans to fence the... (answered by ankor@dixie-net.com)
A wire 20 feet long is to be cut into two pieces. one pierce will be shaped as a square... (answered by josmiceli)