Question

ABC is an equilateral triangle of side 12cm . If AD is the perpendicular drawn from A on BC , find the length of AD​

Answer 1

AD = 12 cm

since, it is a equilateral triangle.

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Answer 2

Answer:

Step-by-step explanation:

There is too many method for solving this:

1st Method

As ABC is an equilateral  Triangle so any line drawn from any corner perpendicular to opposite side the this line divide the opposite line into 2 equal parts.

Here

AD ⊥ BC so BD=DC

now consider rtΔ ADC,

∠ADC= 90

AC=12cm

BD=DC=12/2=6cm

now by using pythagoras theorem

AC²=DC²+AD²

or, 12²=6²+AD²

⇒ 144 = 36+AD²

or, AD² = 144-36

or, AD² =  108

or, AD = √108

or, AD = √(6×6×3) = 6√3 cm

hence, required length of AD is 6√3 cm..

2nd Method

As ABC is an equilateral  Triangle so all ∠s are equal. (=60)

Here

AD ⊥ BC so BD=DC

now consider rtΔ ADC,

∠ADC= 90

AC=12cm

∠ACD = 60°

now,

In ΔADC,

sin60 = AD/AC

or, √3/2 = AD/12

0r, AD = √3/2 × 12 = 6√3 cm

Hence, AD =6√3 cm