To determine which equation to use to find the length \( DP \) in triangle \( DRP \) with given sides \( RP = 5.8 \) and \( DR = 9.6 \), we need to know the relationship between these sides based on the triangle's configuration.
Assuming \( D, R, \) and \( P \) are points in a triangle and \( DP \) is the side opposite the angle formed by the lengths \( DR \) and \( RP \), we can apply the Pythagorean theorem if \( D, R, \) and \( P \) form a right triangle. This would suggest:
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If \( DP \) is the side opposite the hypotenuse \( DR \), and \( RP \) is one of the other sides, you would set it up as: \[ DP^2 + RP^2 = DR^2 \] This translates into: \[ x^2 + 5.8^2 = 9.6^2 \] where \( x = DP \).
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Conversely, if \( DR \) were the hypotenuse, you would use: \[ RP^2 + DP^2 = DR^2 \] which translates to: \[ 5.8^2 + x^2 = 9.6^2 \]
Given the choices you provided, the best option for finding \( DP \) using the Pythagorean theorem (assuming \( DR \) is the hypotenuse) is: \[ 5.8^2 + x^2 = 9.6^2. \]
So, the correct setup to find \( DP \) is: 5.8^2 + x^2 = 9.6^2.