Bully's issues

Question

When Bully folds a square piece of paper in half either horizontally or vertically, the resulting rectangle has a perimeter of 39cm. In square centimeters, what is the area of the original square piece of paper that Bully folded? What are the dimensions of the rectangle and the original square?

Answer 1

Hi Justin,

 

To answer this question, we can follow the steps below:

1. Recall that the perimeter of a square is the sum of the length of its sides. Since all the sides of a square are of equal length, we can call the length of each individual side x. The perimeter of the original square would be 4x (since x + x + x + x = 4x).
2. When the square is folded in half, two of the sides of the resulting rectangle remain length x, and the other two sides become length 1/2x (half the length of the original side of the square). Written in terms of x, the perimeter of the resulting rectangle would thus be x + x + 1/2x + 1/2x. We can simplify this to Perimeter of Rectangle = 3x.
3. The question states that the perimeter of the resulting rectangle is 39cm. To calculate x (the length of a side of the original square), we can plug 39cm in for the Perimeter of the Rectangle. 39cm = 3x. Dividing both sides of the equation by 3, we can solve for x. x = 13cm.
4. The question asks for the area of the original square piece of paper. Since Area of a Square is length times height, and we now know that length and height of this square are both equal to 13cm, we can find the Area. Area = 13cm times 13cm. Thus, the Area of the original square piece of paper = 169 cm². 
5. The question also asks for the dimensions of the original square. We now know that each side of the original square piece of paper is 13cm, so the Dimensions of the Square are 13cm by 13cm.
6. The questions also asks for the dimensions of the rectangle. Since we know that two sides of the rectangle are the same as the length of a side of the square (13cm) and that the other two sides are half the length of one side of the square (13cm divided by 2 = 6.5cm), the Dimensions of the Rectangle are 13cm by 6.5cm.

 

Hope this helps!

Joanna