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in Pythagoras Theorem by (47.6k points)
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Find the length of the side and perimeter of an equilateral triangle whose height is √3 cm.

1 Answer

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by (46.9k points)
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Best answer

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 = (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 respectively.

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