If you reduce the side of a square by 8 cm, you will get a square

If you reduce the side of a square by 8 cm, you will get a square, the area of which is 352 cm ^ 2 less than the area of this square. Find the side of this square.

Let the side of the square be x. Then the area of the original square will be:

x2 = S

Reduce the side of the square by 8: x – 8. write down the expression for finding its area and equate this expression to the area reduced by 352 cm2, which is given by the condition:

(x – 8) ^ 2 = S – 352.

Substitute the S value from the first expression into the second expression:

(x – 8) ^ 2 = x ^ 2 – 352.

Let’s open the brackets and solve this equation:

x ^ 2 – 16x + 64 = x ^ 2 – 352;

x ^ 2 – x ^ 2 – 16x = – 352 – 64;

16x = 288;

x = 18 cm side of the square.

Answer: the side of the square is 18 cm.