∆ABC is an equilateral triangle. point P is on base BC such that PC = 1/2 BC. if Ab = 12cm . find AP
Answers
Answer:
ABC is an equilateral triangle. Since, ABC is an equilateral triangle, OA is the perpendicular bisector of BC. Hence, AP = 2 cm.
Answer:
Refers to the attachment for the Question.
Construction ⇒ Draw the Perpendicular from the point A to the Base BC.
Solution ⇒
∵ All the sides of the Equilateral Triangles are equal,
∴ AB = BC = AC = 6 units.
Also,
PC = 1/3 BC
= 1/3 × 6
= 2 units.
We know Perpendicular in the Equilateral triangles bisects the opposite sides,
∴ QB = QC.
= 1/2 × BC.
= 1/2 × 6
= 3 units.
In Δ AQB,
Applying Pythagoras Theorem,
AB² = BQ² + AQ²
⇒ (6)² = (3)² + AQ²
⇒ AQ² = 36 - 9
⇒ AQ² = 27
⇒ AQ = 3√3 units.
In ΔAQP,
PQ = QC - PC
= 3 - 2
= 1 units.
Applying Pythagoras Theorem,
AP² = PQ² + AQ²
⇒ AP² = (1)² + (3√3)²
⇒ AP² = 1 + 27
⇒ AP = √28
⇒ AP = 2√7 units.
Hence, the length of the AP is 2√7 units.
Hope it helps.