The rectangle has a perimeter of 10.6 cm and an area of 6.72 cm. Determine the sides of the rectangle.

As you know, the perimeter of a rectangle is calculated by the formula: P = (a + b) * 2, where a is the length of the rectangle, b is the width of the rectangle.
Substitute all known values ​​into the formula: 106 = (a + b) * 2.
As you know, the area of ​​a rectangle is calculated by the formula: S = a * b, where a is the length of the rectangle, b is the width of the rectangle.
Substitute all known values ​​into the formula: 672 = a * b.
a = 672 / b.
Substitute instead of a into the perimeter formula and find side b: (672 / b + b) * 2 = 106.
1344 / b + 2b = 106.
1344 + 2b² = 106b.
2b² – 106b + 1344 = 0.
D = b² – 4ac = 11 236 – 4 * 2 * 1344 = 11 236 – 10 752 = 484.
x1 = (-b + √D) / 2a = (106 + 22) / 2 * 2 = 128/4 = 32.
x2 = (-b – √D) / 2a = (106 – 22) / 2 * 2 = 84/4 = 21.
Side b is either 32 mm or 21 mm.
Find the side a = 672/32 = 21 mm.
Let’s check: 21 * 32 = 672. (21 + 32) * 2 = 106.
Answer: The first side of the rectangle is 32 mm = 3.2 cm, the second side is 21 mm = 2.1 cm.