Question

ΔABC is an equiteral triangle point p in a base BC such that PC 1/2 BC, if AB=6 cm find Ap​

Answer 1

Answer:

△ABC is an equilateral triangle. Point P is on base BC. [ Given ]

PC=

3

1

BC,AB=6cm [ Given ]

Here, PC=

3

1

×BC=

3

1

×6

∴ PC=2cm

RC=

2

1

×BC=

2

1

×6

∴ RC=3cm

RP=RC−PC=3−2

∴ RP=1cm ------ ( 1 )

⇒ Altitude AR=

2

3

×a [ a=length of side ]

⇒ AR=

2

3

×6=3

3

Now, in △ARP,

(AP)

2

=(AR)

2

+(RB)

2

AP=

(3

3

)

2

+(1)

2

AP=

27+1

∴ AP=2

7

cm

solution