If the side of a square increases by a factor of 3, by what factor does the area of the square increase?
3s*3s / s*s = 9
The scale drawing of a rectangular playground is shown.On the scale drawing of the playground, 1 inch equals 5 feet.
What are the actual dimensions of the playground?
To find out the factor by which the area of the square increases when the side length is multiplied by a factor of 3, we can use the formula for the area of a square.
The area of a square is given by the formula: A = side^2
Let's assume the original side length of the square is "s". When the side length is multiplied by a factor of 3, the new side length becomes 3s.
The new area of the square can be determined by substituting the new side length into the area formula:
A_new = (3s)^2
= 9s^2
Comparing the original area (A) to the new area (A_new), we can calculate the factor by which the area increases:
Factor = A_new / A
= (9s^2) / (s^2)
= 9
Therefore, when the side of a square increases by a factor of 3, the area of the square increases by a factor of 9.