Question

What is the length of an altitude of an equilateral triangle of side 8cm?

(a) 2√3 cm

(b) 3√3 cm

(c) 4√3 cm

(d) 5√3 cm​

Answer 1

Let ABC be an equilateral triangle of side 8 cm

AB = BC = CA = 8 cm. (all sides of an equilateral triangle is equal)

Draw altitude AD which is perpendicular to BC.

Then, D is the mid-point of BC.

∴ BD = CD = ½ BC = 8/2 = 4 cm

Now, by Pythagoras theorem

AB² = AD² + BD²

⇒ (8)² = AD² + (4)²

⇒ 64 = AD² + 16

⇒ AD= √48 = 4√3 cm.

Hence, altitude of an equilateral triangle is 4√3 cm.

Answer 2

Solution :-

Let us assume that, each sides of ∆ABC is equal to 8 cm .

Now, a perpendicular from vertex A to BC is drawn at point D . Since in an equaliteral ∆ , altitude also bisects the base .

then,

→ AD = BD = 8/2 = 4 cm .

Now, in right angled ∆ABD ,

→ AD = √[AB² - BD]² { By pythagoras theorem }

→ AD = √(8² - 4²)

→ AD = √(64 - 16)

→ AD = √(48)

→ AD = √(16 * 3)

→ AD = 4√3 cm (C) (Ans.)

Shortcut :-

→ Length of Altitude = (√3/2) * Side of an equaliteral ∆

→ Length of Altitude = (√3/2) * 8

→ Length of Altitude = 4√3 cm (Ans.)

Learn more :-

In the figure ∠ MNP = 90°, ∠ MQN = 90°, , MQ = 12 , QP = 3 then find NQ .

https://brainly.in/question/47411321

show that AB2 = AD.AC

https://brainly.in/question/47273910