The perimeter of the rectangle is 36cm. find the area of a rectangle if it is known that its sides are related as

The perimeter of the rectangle is 36cm. find the area of a rectangle if it is known that its sides are related as: a) 1: 5 = b) 1: 3 = c) 1: 2 = d) 1: 1 = How does the area of a rectangle change from the first to the last case? Which rectangle has the largest area?

Периметр: P = 2 * (a + b), площадь: S = a * b.

Найдем стороны прямоугольника:

а) 36 = 2 * (a + 5 * a);

12 * a = 36;

a = 36 / 12 = 3.

5 * 3 = 15.

Стороны:  3 и 15 см.

б) 2 * (a + 3 * a) = 36;

8 * a = 36;

a = 36 / 8 = 4,5.

Стороны: 4,5 и 13,5 см.

в) 2 * (a + 2 * a) = 36;

6 * a = 36;

a = 36 / 6 = 6.

Стороны: 6 и 12 см.

Площади равны:

а) S = 3 * 15 = 45 см².

б) S = 4,5 * 13,5 = 60,75 см².

в) S = 6 * 12 = 72 см2.

При равном периметре площадь прямоугольника больше, когда соотношение сторон меньше.