The perimeter of the triangle is 96cm. Find the lengths of its sides if one of them is 40% larger than the other.

If we designate one of the sides as y cm, then if it is known from the condition of the problem that the other side is 40% larger than the first, then it will be equal to:

y + 40 / 100y = 1.4y (cm).

Applying the dependence to determine the perimeter when it is equal to twice the sum of the sides, we get the following equality:

(y + 1.4y) * 2 = 96,

2.4y * 2 = 96,

2.4y = 48,

y = 20.

Then we find that the second side, which is 40% larger, is:

20 + 20 * 0.4 = 28 (cm).

Answer: the large side of the rectangle is 28 cm long, the smaller side is 20 cm long.