The side of one square is 5cm longer than the side of another square. The area of the two squares differ by 85 square centimetres. find the length of the side of the smaller square.
(s+5)^2-s^2=85
s^2+10s+25-s^2=85
10s=110
s=11
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To find the length of the side of the smaller square, let's assume the length of the side of the smaller square is "x" cm. Since the side of the larger square is 5cm longer, the length of the side of the larger square is "x + 5" cm.
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.