The ratio of the lengths of the sides of the rectangle is 4: 5. Find the area of this rectangle if the length of the smaller side is 12cm.

Let’s make a proportion according to the problem statement. Let x be the length of the larger side, then 4: 5 = 12: x. Let’s apply the main property of proportion: the product of the extreme terms is equal to the product of the middle terms of the proportion
4: 5 = 12: x
4 * x = 12 * 5
4x = 60
x = 60/4
x = 15
This means that the large side is 15 cm. The area of the rectangle is equal to the product of its adjacent sides (length and width). So,
S = 12 * 15 = 180 cm ^ 2
Answer: 180 cm ^ 2