The perimeter of a rectangle other than a square is 20 cm. What should be its length

| July 17, 2021 | education

The perimeter of a rectangle other than a square is 20 cm. What should be its length and width so that the square with the largest perimeter can be cut from it?

1. The perimeter of the rectangle is 20 cm.

So the sum of the length and width is 20/2 = 10 cm.

2. All sides of a square are equal.

The perimeter is the sum of the four sides.

3. When cutting a square from a rectangle, the side of the square is equal to the width of the rectangle.

4. For the square to be cut, the length must be greater than the width.

5. Let’s calculate the possible options, taking into account the previous conditions.

If the width is 1 cm, then the length is 10 – 1 = 9 cm. The perimeter of the square is 1 * 4 = 4 cm.

If the width is 2 cm, then the length is 10 – 2 = 8 cm. The perimeter of the square is 2 * 4 = 8 cm.

If the width is 3 cm, then the length is 10 – 3 = 7 cm. The perimeter of the square is 3 * 4 = 12 cm.

If the width is 4 cm, then the length is 10 – 4 = 6 cm. The perimeter of the square is 4 * 4 = 16 cm.

If the width is equal to another value (5 cm, 6 cm, and so on), the length is either equal to or less.

In the latter case, the perimeter is the largest.

Answer: The original rectangle should be 6 cm long and 4 cm wide.



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