A square has X cm each side. If each side of the square is increased by 4 cm, the are us increased by 392 cm^2 . Calculate x.

Answer 1

Let's start by using the formula for the area of a square, which is A = s^2, where A is the area and s is the length of a side.

If the length of each side of the square is increased by 4 cm, then the new length of a side is x + 4 cm. The new area of the square is (x + 4)^2.

We know that the area is increased by 392 cm^2, so we can set up an equation:

(x + 4)^2 - x^2 = 392

Expanding the left side of the equation, we get:

x^2 + 8x + 16 - x^2 = 392

Simplifying, we get:

8x + 16 = 392

Subtracting 16 from both sides, we get:

8x = 376

Dividing both sides by 8, we get:

x = 47

Therefore, the length of each side of the original square is 47 cm.