What are the sides of a rectangle if its area is 12 cm and the perimeter is 26 cm?

1. Let’s denote the lengths of the sides of the rectangle by X and Y.

2. Using the formula for finding the area of a rectangle, we write the expression:

X * Y = 12

3. Using the formula for finding the perimeter of a rectangle, we write the expression:

2 * (X + Y) = 26.

4. Find X and Y. Let us express Y through X from the perimeter formula:

X + Y = 13;

Y = 13 – X.

5. Substitute in the area formula Y, expressed through X, and solve:

X * (13 – X) = 12;

13X – X ^ 2 – 12 = 0;

X ^ 2 – 13X + 12 = 0;

D = 13 ^ 2 – 4 * 12 = 121;

X1 = (13 + √121) / 2 = 12;

X2 = (13 – √121) / 2 = 1;

Y1 = 13 – 12 = 1;

Y2 = 13 – 1 = 12.

Answer: the sides of the rectangle are 12 cm and 1 cm.