Question

In equilateral ∆ABC length of the side is a. The perpendicular to side AB at point B intersects the extension of median AM in point P. What is the perimeter of ∆ABP, if MP = b?

Answer 1

Answer:

Perimeter  = a + b + sqrt ( (a^2/4) + b^2 ) + sqrt(3)a/2

Step-by-step explanation:

Givens

• ΔABC is equilateral
• AB = a
• The diagram is given below
• AM is a Median
• PB ⊥ AB
• PM = b

Find

Perimeter of ΔPBM

Formula

Perimeter of ABM = AB + PB + PM + AM

Solution

• AB = a                     Given
• PM = b                     Given
• PB = sqrt( (a/2)^2 + b^2)
• PB = sqrt( a^2/4   + b^2)    PMB is a right angle  Pythagoras applies.
• AM = sqrt( AB^2 - BM^2)  AMB is a right angle Pythagoras applies.
• AM = sqrt(a^2 - (a/2)^2 ) = sqrt(3)a/2

Perimeter  = a + b + sqrt ( (a^2/4) + b^2 ) + sqrt(3)a/2   Answer