# The perimeter of the rectangle is 32 cm. Find the sides of the rectangle if its area is 39 cm2.

Given:
Rectangle;
Perimeter = 32 cm;
Area = 39 cm ^ 2;
Find the sides of a rectangle;

Decision:
Let x be one side of the rectangle;
y – the other side of the rectangle, not equal to the side x;
Since, perimeter = 2 * (x + y), and area = x * y;
Then, substituting the known values, we get:
32 = 2 * (x + y);
39 = x * y;
We got a system of equations:
Let’s solve it and find x and y.
1) From the first 32 = 2 * (x + y);
x + y = 32/2;
x + y = 16;
x = 16 – y;
2) Substitute in the second equation:
39 = x * y;
39 = (16 – y) * y;
39 = 16 * y – y ^ 2;
39 – 16 * y + y ^ 2 = 0;
Hence, y1 = 3 and y2 = 13;
3) x1 = 16 – y1 = 16 – 3 = 13;
x2 = 16 -y2 = 16 – 13 = 3;
This means that the sides of the rectangle are 3 cm and 13 cm.
Answer: 3 cm and 13 cm.

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