Question

∆ABC is an equilateral triangle. Point P is on base BC such that

PC = 1/3 BC. If AB = 12 cm, find AP.​

Answer 1

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Answer 2

Explanation:

In equilateral triangle all sides are equal to each other .

∆ABC is an equilateral triangle

so, let D is midpoint which is drawn from A Vertex to midpoint( D) at opposite side of vertex A

so, an equilateral triangle divided into two equal parts and AD is median of ∆ ABC.

so, given that AB = 12cm therefore , BC is divided into two equal parts. so, finally BD= 6cm

( because one side of quil. ∆ is 12cm and when we do half of it BD become 6 cm).

BD = 6cm and DC = 6 cm.

(here AD is height of equilateral triangle .)

therefore , we apply pythagoras theorem

so, (hypotenuse ) ^2 = ( perpendicular )^2 + (base)^2

so, (AB)^2 = (AD)^2 + (DC )^2

therefore , (12)^2 = (AD)^2 + (6)^2

(AD)^ 2 = (12)^2 - (6)^2

so, (AD )^2 = 144 - 36

so, (AD)^2 = 108cm

AD = √ 108cm

so, AD = 6√3cm . so, height = 6√3 cm