Problema Solution
If you fold a square paper vertically, the new rectangle has a perimeter of 39 inches.
What is the area of the original square?
What is the perimeter if the original square?
What is the area of the resulting rectangle?
Make a ratio of areas and perimeters. What do you notice?
Answer provided by our tutors
Let 'a' represent the length of the square's side.
The perimeter of the new rectangle is 39 in means:
2(a + a/2) = 39
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click here to see the equation solved for a
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a = 13 in
What is the area of the original square?
A = a^2
A = 13^2
A = 169 in^2
The area of the original square is 169 in^2.
What is the perimeter of the original square?
P = 4a
P = 4*13
P = 52 in
The perimeter of the original square is 52 inches.
What is the area of the resulting rectangle?
A = a*(a/2)
A = 13*(13/2)
A = 84.5 in^2
Make a ratio of areas and perimeters.
Area of square : Area of rectangle = 169 : 84.5 = 2
Perimeter of square : Perimeter of rectangle = 52 : 39 = 4 : 3
What do you notice?
The area of the rectangle is 2 times smaller than the area of the square.
The perimeter of the rectangle is 3/4 of the square's perimeter.