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(s+5)^2-s^2=85
s^2+10s+25-s^2=85
10s=110
s=11
check my work
s^2+10s+25-s^2=85
10s=110
s=11
check my work
The area of a square is calculated by multiplying the length of one side by itself. So, the area of the smaller square is x * x = x² square cm, and the area of the larger square is (x + 5) * (x + 5) = (x + 5)² square cm.
The problem states that the difference in area between the two squares is 85 square cm. So, we can set up an equation:
(x + 5)² - x² = 85
Expanding the equation:
x² + 10x + 25 - x² = 85
Simplifying the equation:
10x + 25 = 85
Subtracting 25 from both sides:
10x = 60
Dividing both sides by 10:
x = 6
Therefore, the length of the side of the smaller square is 6 cm.