The perimeter of the rectangle is 60 cm and one side of it is 4 times larger than the other; the perimeter of the square is 52 cm.

The perimeter of the rectangle is 60 cm and one side of it is 4 times larger than the other; the perimeter of the square is 52 cm. Find the area difference between the rectangle and the square.

a, b are the sides of the rectangle.
Let side a be x cm, and side b 4 times larger, which means 4 x cm.
P = 2 * (a + b);
60 = 2 * (x + 4 x);
60 = 2 x + 8 x;
2 x + 8 x = 60;
10 x = 60;
x = 60: 10;
x = 6 cm side a.
6 * 4 = 24 cm side b.
S = a * b.
S = 6 * 24;
S = 144 cm² of the first rectangle.
P square = 4 * a;
P = 52 cm,
52 = 4 * a;
4 a = 52;
a = 52: 4;
a = 13 cm side of a square, the perimeter of which is 52 cm.
Let’s find the area of this square.
S = 13 * 13;
S = 169 cm².
Let’s find the difference in area.
169 – 144 = 25 cm.
Answer: 25 cm difference between the areas of a rectangle and a square.