The perimeter of a rectangle, the length of which is 6 cm longer than its width, is 52 cm. How many square centimeters

The perimeter of a rectangle, the length of which is 6 cm longer than its width, is 52 cm. How many square centimeters is the area of the square, with the perimeter, equal to the perimeter of the rectangle, more than the area of the rectangle?

As you know, the perimeter of a rectangle is P = 2 * (a + b), where a is the length of the rectangle, b is its width.

By the condition of the problem a = b + 6, we find what the width of the rectangle is equal to:

2 * (b + 6 + b) = 52,

2 * b + 6 = 52: 2.

2 * b = 26 – 6,

b = 20: 2,

b = 10 (cm).

Therefore, the length of the rectangle is a = 10 + 6 = 16 (cm).

Let’s find the area of ​​the rectangle:

S = a * b = 10 * 16 = 160 (cm²).

By the condition of the problem, the perimeter of the square is also 52 cm.

Since the perimeter of the square is: P = 4 * a, the side of the square will be:

a = 52: 4 = 13 (cm).

Find the area of ​​the square:

S = a² = 13² = 169 (cm²).

Now we can find how much the area of ​​the square is larger than the area of ​​the rectangle:

169 – 160 = 9 (cm²).

Answer: 9 cm².