What is the largest square of which the dimensions are natural numbers that you can cut from the corners of 20cm x 20cm paper? Explain
So let's cut out an x by x square from each corner.
so the base we would be left with would be an
(20-2x) by (20-2x) cm
but 20-2x > 0
-2x > -20
x < 10,
since you want x to be a natural number, that would be a 9 by 9 cm square
Thanks reiny
To determine the largest square that can be cut from the corners of a 20cm x 20cm paper, we need to find the side length of the square first.
We can start by figuring out how much paper would be left after cutting the corners. Since the paper is a square with side length 20cm, cutting the corners would result in a square with side length reduced by the same size on all four sides.
Let's denote the side length of the square to be cut from the corners as x cm. The resulting square would then have sides of (20cm - 2x) cm.
Since we want to find the largest square that can be cut, we need to maximize the side length of the square, which is (20cm - 2x) cm.
Now, we know that the side length of a square cannot be negative, so (20cm - 2x) cm should be greater than or equal to 0:
20cm - 2x ≥ 0
To solve this inequality, we can isolate x on one side:
2x ≤ 20cm
Dividing both sides of the inequality by 2 gives us:
x ≤ 10cm
Here, we find that x should be less than or equal to 10cm. Since x represents the length of the side to be cut from each corner, it cannot be greater than half of the original side length, which is 10cm in this case.
Therefore, the largest square you can cut from the corners of a 20cm x 20cm paper would have a side length of 10cm.