22 If right triattgle \( A B C \) has sides \( b=7 \) and \( c=24 \), then which of the follarwing is a possible value for the perimeter of triangle \( A B C \) ? A) 50 B) 25 C) 56 D) 84

To determine a possible perimeter for the right triangle \( \triangle ABC \) with sides \( b = 7 \) and \( c = 24 \), we can use the Pythagorean theorem. Assuming that the right angle is at vertex \( A \), sides \( b \) and \( c \) are the legs of the triangle, and side \( a \) (opposite the right angle) is the hypotenuse. Using the Pythagorean theorem: \[ a^2 = b^2 + c^2 \] \[ a^2 = 7^2 + 24^2 \] \[ a^2 = 49 + 576 \] \[ a^2 = 625 \] \[ a = \sqrt{625} = 25 \] Now, the perimeter \( P \) of the triangle is the sum of all its sides: \[ P = a + b + c = 25 + 7 + 24 = 56 \] Therefore, the possible perimeter of triangle \( ABC \) is **56**. **Answer:** C) 56