Question

Find the perimeter and area of an equilateral triangle whose height is 12 cm. Write your
answers, correct to two decimal places,​

Answer 1

Given :

• Height of equilateral triangle = 12 cm

To Find :

• Perimeter of the triangle
• Area of the triangle

Solution :

Side ( a ) = ( 2h ) /√3

➨ a = ( 2 × 12 ) / √3

➨ a = ( 8 × 3 ) / √3

➨ a = 8√3 cm

Perimeter of equilateral triangle = 3a

➨ 3 × 8√3

➨ 24√3 cm

Area = ( √3 / 4 ) a²

➨ ( √3 / 4 ) ( 8√3 ) ²

➨ (√3 / 4 ) ( 192 )

➨ 48√3

➨ 82.13 cm²

Answer 2

Answer:

Perimeter = 41.57 cm

Area = 83.14 sq. cm

Step-by-step explanation:

Let the sides of eq. ∆ be x

Height = 12cm ( Given )

Side of eq. ∆ = 2h / √3 ( h = height )

x = 2×12/√3

x = 2×4×3/√3

x = 8×√3×√3 / √3

x = 8√3

Now,

Perimeter of eq.∆ = 3 × side

= 3 × 8√3

= 24√3

= 24 × 1.732 ( √3 = 1.732)

= 41.568

= 41.57 Ans...

And,

Area of eq.∆ = (√3/4 ) × side^2

= √3/4 × 8√3 ×8√3

= √3 × 2√3 × 8√3

= 48√3 sq. cm

= 48 × 1.732 ( √3 = 1.732)

= 83.136

= 83.14 sq. cm Ans...

Hope it helps you...

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