Question

(1) In ∆ABC is an equilateral triangle. Point P is on base BC such that bc 1/3 Bc if AB is 9​

Answer 1

Answer:

AABC is an equilateral triangle. It is given that,

1 PC= BC 3

1 ⇒ PC × 6 = 3

⇒PC 2cm =

⇒BP = 4cm

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

:: OC = 3 cm

→ OP = OC - PC

= 3-2

= 1

...(1)

Now, According to Pythagoras theorem, In ΔΑΟΒ,

AB²= AO² + OB² ⇒ (6)² = AO² + (3) ²

⇒ 36 - 9 = AO² ⇒ AO² = 27

⇒ AO = 3√√/3cm... (2)

In ΔΑΟΡ,

AP² = AO² + OP²

⇒ AP² = (3√3)² + (1)² (From (1)²

⇒ AP² - 27 +1

⇒ AP² = 28

⇒ AP = 2√7cm

Hence, AP = 2√7 cm.