Given a rectangle, the perimeter of which is 30 cm What should be the sides of this rectangle

Given a rectangle, the perimeter of which is 30 cm What should be the sides of this rectangle in order for its area to be the largest?

We denote by a and b the adjacent sides of the rectangle, then

2 * (a + b) = 30; a + b = 15; b = 15 – a.

S = ab = a * (15 – a).

1) If a = 5 cm, then b = 15 – 5 = 10 (cm), S = 5 * 10 = 50 (cm2).

2) If a = 14 cm, then b = 15 – 14 = 1 (cm), S = 14 * 1 = 14 (cm2).

3) If a = 13 cm, then b = 15 – 13 = 2 (cm), S = 13 * 2 = 26 (cm2).

Conclusion: Of the three options, a rectangle with sides equal to 5 cm and 10 cm has the largest area.