Paul had a square piece of paper.He cut out a rectangle from the paper that was 4 centimetres by 9 centimetres. The area of the left over paper was 108 square centimetres. What was the length of the sides of Paul’s original square?
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Paul starts with a square piece of paper. He cuts out a rectangle that measures 4 centimeters by 9 centimeters. After cutting, the remaining paper has an area of 108 square centimeters. We need to find the side length of the original square.
First, we calculate the area of the rectangle that was cut out. The rectangle measures 9 centimeters by 4 centimeters. Using the formula for area, we multiply length times width: 9 times 4 equals 36 square centimeters.
Next, we find the total area of the original square by adding the area of the cut-out rectangle to the leftover area. We have 36 square centimeters from the rectangle plus 108 square centimeters of leftover paper, which gives us a total of 144 square centimeters.
Finally, we find the side length of the original square. Since the area of a square equals side squared, we have 144 equals side squared. Taking the square root of 144 gives us 12. Therefore, the side length of Paul's original square was 12 centimeters.
Let's review our solution. We calculated the rectangle area as 36 square centimeters, added the leftover area of 108 square centimeters to get a total of 144 square centimeters, and found the side length by taking the square root of 144. The answer is 12 centimeters for the side length of Paul's original square.