Question

∆ABC is an equilateral triangle point p is on base BC such that BC is equal to 1/3 BC. If AB = 12cm. Find AP.
4 points

Answer 1

Answer:

4√7 cm

Step-by-step explanation:

∆ABC is an equilateral triangle.

It is given that,

PC=1/3 BC

AB=BC=CA= 12cm (equilateral triangle)

so, PC = 1/3.12= 4cm

and BP= 12-4= 8cm

Since, ABC is an equilateral triangle, OA is the perpendicular bisector of BC.

so, OC = 6 cm

=> OP= OC-PC

=>OP= 6-4= 2cm

Now, According to Pythagoras theorem,

In ∆AOB,

AB²= AO² + OB²

=> (12)² = AO² + (6) ²

=> 144 - 36 = AO²

=> AO² = 108

=> AO = 6√3 cm

In ∆AOP,

AP² = AO² + OP²

=> AP² = (6√3)² + (2)²

=>AP²= 108 +4

=> AP² = 112

=> AP = 4√7cm

Hence, AP =4√7 cm