Given pa=7 in. and cb=11 in. what is ca ?

The answer is 11 inches.

The length of CA is 11 in.  

Step-by-step explanation:

We need to find the length of CA of provided figure

Given:- AP = PB  , CB = 11 in. and ∠CPB =90°

In triangle ΔAPC and ΔBPC

CP =CP ( common )

Since, AP = PB

⇒ PB = 7 in.

In ΔBPC

By pythagoras ( since ΔBPC is right angle at ∠P )

(prependicular)² + (base)² = (hypoteneous)²

                     (CP)² + (PB)²  = (CB)²

                      (CP)² + (7)²  = (11)²

                       (CP)² + 49  = 121

Subtract both the sides by 49, in above

                (CP)² + 49 - 49  = 121 - 49

                               (CP)²   = 72

                                 CP = √72

In ΔAPC

By pythagoras ( since ΔAPC is right angle at ∠P )

(prependicular)² + (base)² = (hypoteneous)²

                     (CP)² + (PA)²  = (CA)²

                      (√72)² + (7)²  = (CA)²

                           72  + 49  = (CA)²

                                    121  = (CA)²

                                   √121 = CA

                                        11 = CA

Therefore, The length of CA is 11 in.

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