Question

triangle ABC is an equilateral triangle point P is on the base BC such that BC is equal to one third BC if ab is equal to 6 find AP​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer

Given:- an equilateral triangle ABC

, a point P on BC such that BP=1/3 BC

AB=6 units

To find:- the length of AP

Construction:- An altitude from point A

intersecting BC at O

Solution:-

ABC is an equilateral triangle (given)

AB = 6 (given)

therefore,

BC=6(sides of an equilateral triangle are equal)

So BP = (1/3)*BC = (1/3)*6 = 6/3 = 2

In an equilateral triangle, the altitude and the median coincide so AO is the altitude by construction and also the median

So, BO = OC ... (1)

BO+OC=BC ... (2)

Putting (1) in (2) we get BO+BO=BC

=> 2BO=BC

=> BO=BC/2= 6/2= 3

Since BP =2 and BO=3

,OP=BO-BP=3-2=1

so OP = 1

AO is the altitude by construction so angle AOB is equal to 90 degrees hence triangle AOB is a right angle triangle

So AO² + OB² = AB² (pythagoras theorem)

putting values of AB=6 and OB= 3

We get that AO=√27 =3√3

Since AO is the altitude angle AOP is also equal to 90 degrees and hence triangle AOP is also a right angle triangle

So by pythagoras theorem we get that

AP² = AO²+OP²= (3√3)² + 1²

=> AP² = 27+1 = 28

=> AP = √28

=> AP = 2√7 which is approximately equal to 5.29

Hope this helps

Thanks