Question

find the length of the side of an equilateral traingle whose height is √3​

Answer 1

Question:--

Find the length of the side of an equilateral traingle whose height is √3

Answer:

AD ⊥ BC, B – D – C.

In ∆ABD, ∠B =60° ,

∠ADB = 90°

∴ ∠BAD = 30° [Remaining angle of a triangle]

∴ ∆ABD is a 30° – 60° – 90° triangle.

∴ AD = √3/2 AB [Side opposite to 600]

∴ √3 = (2√3)/√3 AB

∴ AB = (2√3)/√3

∴ AB = 2cm

∴ Side of equilateral triangle = 2cm

Perimeter of ∆ABC = 3 × side

= 3 × AB = 3 × 2 = 6cm

∴ The lenght of the side and perimetter of the equilaterral triangle are 2 cm and 6 cm