The perimeters of two squares are 40cm and 30cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

Step 1: Find the sides of the first two squares.

The side of a square is equal to its perimeter divided by 4. Therefore, the sides of the first two squares are:

Side of square 1 = 40cm / 4 = 10cm Side of square 2 = 30cm / 4 = 7.5cm

Step 2: Find the areas of the first two squares.

The area of a square is equal to the side of the square squared. Therefore, the areas of the first two squares are:

Area of square 1 = 10cm * 10cm = 100cm² Area of square 2 = 7.5cm * 7.5cm = 56.25cm²

Step 3: Find the difference of the areas of the first two squares.

The difference of the areas of the first two squares is:

Difference of areas = Area of square 1 - Area of square 2 = 100cm² - 56.25cm² = 43.75cm²

Step 4: Find the side of the third square.

The side of the third square is equal to the square root of the difference of the areas of the first two squares. Therefore, the side of the third square is:

Side of square 3 = √43.75cm² = 6.625cm

Step 5: Find the perimeter of the third square.

The perimeter of the third square is equal to the side of the third square multiplied by 4. Therefore, the perimeter of the third square is:

Perimeter of square 3 = 6.625cm * 4 = 26.5cm

Answer: 24cm