Question

find the length of the side and perimeter of an equilateral triangle whose hight is root 3 cm
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Answer 1

Answer:

Here is your answer

Step-by-step explanation:

Let ∆ABC be the given equilateral triangle.

∴ ∠B = 60° [Angle of an equilateral triangle]

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 = 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 respectively.