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

January 29, 2021 | education

| 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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