To determine the lengths of the sides \( R \), \( S \), and \( T \) of the right triangle formed by three squares, we can use the relationship between the side lengths of a right triangle and the areas of the squares:
- Let the areas of the squares on the sides \( R \), \( S \), and \( T \) be represented as \( A_R \), \( A_S \), and \( A_T \), respectively.
- Since the area of a square is equal to the side length squared, we have: \[ A_R = R^2, \quad A_S = S^2, \quad A_T = T^2 \]
- For a right triangle, we can use the Pythagorean theorem, which states: \[ R^2 + S^2 = T^2 \]
- Substituting the areas into this equation, we get: \[ A_R + A_S = A_T \]
From the established relationships, we can express the side lengths as follows:
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The length of side \( R \) is: \[ R = \sqrt{A_R} \]
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The length of side \( S \) is: \[ S = \sqrt{A_S} \]
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The length of side \( T \) is: \[ T = \sqrt{A_T} \]
By determining the areas you have for each of the squares formed on sides \( R \), \( S \), and \( T \), substitute those values into the equations above to calculate the side lengths \( R \), \( S \), and \( T \).
If you provide specific values for the areas of the squares \( A_R \), \( A_S \), and \( A_T \), I can help you compute the lengths of sides \( R \), \( S \), and \( T \).