x^2 + 7^2 = 24^2

Question

What is DP? Round your answer to the nearest tenth if necessary(2 points)
DP =

Answer 1

To solve for \( DP \) in the equation \( x^2 + 7^2 = 24^2 \), we can first simplify the equation step by step.

1. Calculate \( 7^2 \) and \( 24^2 \):

   \[ 7^2 = 49 \] \[ 24^2 = 576 \]

2. Substitute these values back into the equation:

   \[ x^2 + 49 = 576 \]

3. To isolate \( x^2 \), subtract 49 from both sides:

   \[ x^2 = 576 - 49 \] \[ x^2 = 527 \]

4. Now, take the square root of both sides to find \( x \):

   \[ x = \sqrt{527} \]

5. To calculate \( \sqrt{527} \):

   \[ \sqrt{527} \approx 22.9 \]

Thus, after rounding to the nearest tenth, we find:

\[ DP \approx 22.9 \]

Final answer:

\[ \boxed{22.9} \]