Question

5. Find the length of the side
and perimeter of
equilateral triangle whose height is √3 cm​

Answer 1

Answer:

6cm

Step-by-step explanation:

Let ∆ ABC is equilateral triangle.

Seg AD is median.

Therefore in ∆ ABC,

Angle A=30 (as AD is median)

Angle B=90(as AD is median)

Angle C=60(as ∆ABC is equilateral triangle)

Therefore by 30-60-90 theorem.

AD=✓3/2 ×AC

✓3 = ✓3/2 × AC

✓3×2/✓3 = AC

Therefore 2cm = AC

it is equilateral triangle,

Therefore perimeter=3×side

=3×2cm

= 6cm

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Answer 2

Answer:

Side = 2 cm, Perimeter = 6cm

Step-by-step explanation:

Since, ABC is an equilateral triangle, CD is the perpendicular bisector of AB.

Now according to Pythagoras Theorm,

In ∆ACD

AC^2 = AD^2 + CD^2

=>(2a)^2 = a^2 + (√3)^2

=>4a^2 - a^2 = 3

=>3a^2 = 3

=>a^2 = 1

=>a = √1 = 1 cm.

hence side = 2cm (1+1)

perimeter = ( 2 + 2 + 2 ) cm = 6 cm