The width of the rectangle is 26cm. How much will the area of the rectangle increase if the length is increased by 2 cm.

Let us express the area of ​​a rectangle with a width of 26 cm (b = 26 cm):
S1 = a * b = 26 * a.

Let us express the area of ​​a rectangle with a length increased by 2 cm and a width equal to 26 cm:
S2 = a * b = (a + 2) * 26 = 26 * a + 52.

To determine by how many units one quantity is greater (or less) than another, it is necessary to subtract another from one quantity.
If the difference is greater than 0, then the first value is greater than the second; if the difference is less than 0, then the first value is less than the second; if the difference is 0, then both values ​​are equal.

Let’s calculate how much S2 is more than S1:

S2 – S1 = 26 * a + 52 – 26 * a = 52 (units ^ 2).

Answer: the area of ​​the rectangle will increase by 52 units ^ 2.