Answer:
Perimeter = (2 + √3)·a
Step-by-step explanation:
Given: ΔABC is equilateral and AB = a
The diagram is given below :
AM is a median , PB ⊥ AB , PM = b
Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.
We get, ∠AMB = 90°. So, by linear pair ∠AMB + ∠PMB = 180° ⇒ ∠PMB = 90°. Also, ∠ABC = 60° and ∠ABP = 90° (given) So, ∠PBM = 30°
Since, AM is perpendicular bisector of BC. So,
Now in ΔAMB , By using Pythagoras theorem
Now, in ΔBMP :
Perimeter of ABM = AB + PB + PM + AM
Hence, Perimeter of ΔABP = (2 + √3)·a units
