Answer:
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.
