Find the sides of a rectangle if its area is 3 dm2 and the perimeter is 8 dm.

S = a * b ab = 3 dm ^ 2 P = 2 (a + b) = 8 dm Hence the system. {ab = 3 {2a + 2b = 8 {a = 3 / b {2 * 3 / b + 2b = 8 Solve the 2nd level of the system:
6 / b + 2b = 8 6 + 2b ^ 2 = 8b 2b ^ 2-8b + 6 = 0 D = 64-4 * 6 * 2 = 4 ^ 2 b1 = 1 b2 = 3 Substitute in the 1st level of the system:
a = 3, a = 1.
Answer: 1 and 3; 3 and 1.