Answer: Therefore, a possible expression for the length of the side of the square painting is:
side = 15x + 8
or
side = -15x - 8
Explanation:
To find a possible expression for the length of the side of the square painting, we need to use the formula for the area of a square, which is:
Area = side^2
We can set the given expression for the area of the painting equal to this formula:
225x¹+240x+64 = side^2
Next, we can simplify the expression on the left-hand side by factoring it into a perfect square trinomial:
225x¹+240x+64 = (15x + 8)^2
Now we can substitute this expression back into the equation and solve for the side of the square painting:
(15x + 8)^2 = side^2
Taking the square root of both sides, we get:
15x + 8 = side
or
15x + 8 = -side (since the length of a side can be positive or negative)
Therefore, a possible expression for the length of the side of the square painting is:
side = 15x + 8
or
side = -15x - 8
Note that since we are dealing with a geometric object, we should choose the positive value for the length of the side, as the side length cannot be negative. Therefore, the final expression for the length of the side of the square painting is:
side = 15x + 8