The perimeter of the rectangle is 30cm. Find its sides if you know that its area is 56cm ^ 2.

Let x be the length of the rectangle, then
y is the width of the rectangle.
Based on the data in the problem statement, we compose two equations and find the unknown values:
x * y = 56
2x + 2y = 30
From the second equation we express x and substitute it into the first equation:
x = (30 – 2y) / 2
x = 2 (15 – y) / 2
x = 15 – y
(15 – y) * y = 56
15y – y ^ 2 -56 = 0
y ^ 2 – 15y + 56 = 0
D = 225 – 224 = 1
√D = 1
y1 = (15 + 1) / 2 = 8
y2 = (15 – 1) / 2 = 7
Then x1 = 15 – 8 = 7
x2 = 15 – 7 = 8
Answer: The length of the rectangle is 8 cm and the width is 7 cm.