SOLUTION: pierre folded a square piece of paper vertically to make two rectangles. each rectangled had a perimeter of 39 inches. how long is each side of the original square? what is the are

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: pierre folded a square piece of paper vertically to make two rectangles. each rectangled had a perimeter of 39 inches. how long is each side of the original square? what is the are      Log On


   

Question 1067279: pierre folded a square piece of paper vertically to make two rectangles. each rectangled had a perimeter of 39 inches. how long is each side of the original square? what is the area of the original square? what is the area of one of the rectangles?
Found 3 solutions by stanbon, MathTherapy, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
pierre folded a square piece of paper vertically to make two rectangles. each rectangled had a perimeter of 39 inches. how long is each side of the original square? what is the area of the original square? what is the area of one of the rectangles?
-----
Area of the square = x^2
Diameter = sqrt(2)x is the hypotenuse of each of the resulting triangles.
-----
Sides of one of the triangles.
x, x, sqrt(2)x
Equation:
x + x + sqrt(2)x = 39
2x + sqrt(2)x - 39 = 0
(2+sqrt(2))x = 39
x = 39/3.414
x = 11.42
-----
Ans: Area = 11.42*2 = 130.48
--------------
Cheers,
Stan H.
---------------

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

pierre folded a square piece of paper vertically to make two rectangles. each rectangled had a perimeter of 39 inches. how long is each side of the original square? what is the area of the original square? what is the area of one of the rectangles?
Correct answers: Length of each side of original square: highlight_green%28matrix%281%2C2%2C+13%2C+inches%29%29

                 Area of original square: highlight_green%28matrix%281%2C5%2C+13%5E2%2C+or%2C+169%2C+sq%2C+inches%29%29

                 Area of a rectangle: highlight_green%28matrix%281%2C5%2C+169%2F2%2C+or%2C+84.5%2C+sq%2C+inches%29%29

Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.
pierre folded a square piece of paper vertically to make two rectangles. each rectangled had a perimeter of 39 inches.
how long is each side of the original square? what is the area of the original square? what is the area of one of the rectangles?
~~~~~~~~~~~~~~~~~~~~~ 

Let "x" be the half of the size of the original square piece of paper.

Then the perimeter of the rectangle (after the paper folding) is 

2x + x + 2x + x = 39 inches,

6x = 39 inches,

x = 39%2F6 = 6.5 inches.

Then the size of the original square piece of paper is 2x = 2*6.5 = 13 invhes.

The area of the original square is 13%5E2 = 169 square inches.

The are of the rectangle is the half of it, i.e. 169%2F2 = 84.5 square inches.