The sides of the square were increased by 3 times. How many times will the area increase?

1. Let’s designate the side of the first square X. And the area of ​​the first square S1. Then, using the formula for the area of ​​a square, we write:

S1 = X ^ 2.

2. Let’s designate the side of the enlarged square Y. And the area of ​​the enlarged square S2. Then, using the formula for the area of ​​a square, we write:

S2 = Y ^ 2.

3. Since the side of the square was enlarged 3 times, then:

Y = X * 3.

4. Substitute into the formula S2 = Y ^ 2 “Y” expressed through “X” and simplify:

S2 = (X * 3) ^ 2 = 9X ^ 2.

5. Let’s find the ratio of the area S2 to the area S1, as the ratio of their values, expressed in terms of X:

S2 / S1 = 9X ^ 2 / X ^ 2 = 9.

Answer: the area of ​​the square will increase 9 times if its sides are increased 3 times.