Question

Harriet has a square piece of paper.
She folds it in half to form a rectangle and then in half again to form a second rectangle (which is not a square).
The perimeter of the second rectangle is
30 cm
What is the area of the original square?

Answer 1

Given :  Harriet has a square piece of paper. She folds it in half to form a rectangle and then in half again to form a second rectangle (which is not a square). The perimeter of the second rectangle is 30cm

To find : Area  of the original square

Solution:

Let say Side of original Square

= 4A  cm

Hence Area = (4A)² = 16A²   cm²

Then

Square when folded  in half

Then Sides of rectangle  

will be  4A   &  2A

Now again Folded

Sides can be  2A  & 2A    or  4A  & A

2A  & 2A  would be a Square ( its given that its not a square)

Hence Second Rectangle Sides are 4A & A

Perimeter = 2(4A + A) = 10A

10A = 30cm

=> A = 3 cm

Area  of the original square =   16A²  = 16 * 3² = 144 cm²  

area of the original square = 144 cm²  

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