The sides of the rectangle are 2 to 6, and its perimeter is 32 cm. Find the area of this rectangle.

We introduce the coefficient of proportionality x and the sides of this triangle have a length of 2x cm and 6x cm.Let us use the formula for the perimeter of a rectangle and compose the equation:
P = 2 * (2x + 6x) = 32
16x = 32
x = 2.
Knowing the proportionality coefficient, we find the sides of the rectangle:
2 * 2 = 4 (cm);
2 * 6 = 12 (cm).
The sides are known, we find the area by the formula:
S = a * b = 4 * 12 = 48 (cm²).
Answer: the area of the rectangle is 48 cm².

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