The perimeter of the rectangle is 30 cm. Find its sides if you know that the area of the rectangle is 56 cm².

The length of the rectangle is x cm.
The width is equal to y cm.

Let’s compose the equations:
2x + 2y = 30.
x * y = 56.
Let us simplify the first equation and express the length from it:
x + y = 15;
x = 15 – y.
Substitute in the second equation:
y * (15 – y) = 56;
– y2 + 15y – 56 = 0;
y2 – 15y + 56 = 0.
We have a = 1, b = – 15, c = 56.
D = b2 – 4ac = (-15) 2 – 4 * 56 = 225 – 224 = 1.
x1 = (15 + 1): 2 = 8 cm.
x2 = (15 – 1): 2 = 7 cm.
Hence y1 = 15 – 8 = 7 cm.
y2 = 15 – 7 = 8 cm.
Answer: the sides of the rectangle can be 7 and 8 cm or 8 and 7 cm.