# The perimeter of the rectangle is 32 cm and the area is 60 cm2. Find the length and width of the rectangle.

Let us denote the sides of this rectangle by the letters x and y.

Then, according to the problem statement, we can compose the following system of equations:

2 * (x + y) = 32,

x * y = 60

From the first equation we get:

x + y = 16,

y = 16 – x.

Substitute this value into the second equation:

x * (16 – x) = 60,

16 * x – x² = 60,

x² – 16 * x + 60 = 0.

Let’s find the discriminant of this equation:

(-16) ² – 4 * 1 * 60 = 16.

So the equation has the following roots:

x = (16 + 4) / 2 = 10 and x = (16 – 4) / 2 = 6.

So the second side of the rectangle is:

y = 16 – 10 and y = 16 – 6 = 10.

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