Find the area of all possible rectangles with a perimeter of 12 cm, if the length of their sides is expressed as an integer cm. Which rectangle has the largest area.
Divide the perimeter by 2, we get half the perimeter. It will be equal to the sum of the length and width of the rectangle.
p = 12 cm ÷ 2 = 6 cm.
Let’s select the sides of the rectangle, the sum of which is 6 cm, and calculate the area of each pair of sides.
1 cm * 5 cm = 5 cm²
2 cm * 4 cm = 8 cm².
3 cm * 3 cm = 9 cm².
Answer: the largest area is for a rectangle with sides of 3 cm.
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