# The width of the rectangle was increased by 1.5 times. How has its area changed?

**The width of the rectangle was increased by 1.5 times. How has its area changed? Specify the type of relationship between the width and area of the rectangle.**

Answer: the correct answer is option 4) increased by 1.5 times; directly proportional.

The area of a rectangle is defined as the product of its length and width.

S = a * b,

where: S is the area of the rectangle; a – its length; b – width.

Let’s increase the length by 1.5 times, then the area will be:

(1.5 * a) * b.

Let’s transform the expression, since all multiplication actions are equal:

(1.5 * a) * b = 1.5 * a * b = 1.5 * (a * b).

It turned out that we increased the right side of the expression for determining the area by 1.5 times. In order to maintain equality in it, it is also necessary to increase the left side. That is, the area will increase by 1.5 times.

This kind of relationship between one of the terms of the expression and its value, when increasing the first increases and the second (and vice versa) is called directly proportional.

Answer: increased by 1.5 times; directly proportional.