Question

1. Find the height of an equilateral triangle having side 4 cm. ?​

Answer 1

Given:

• Side of the equilateral triangle is 4cm.

To find:

• Height of the equilateral triangle?

Solution:

• Let's consider ABC is an equilateral triangle.

Where,

• Side = 4cm

• Let height of the triangle be h.

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« Now, By using Pythagoras theorem,

→ h² = p² + b²

→ h² = 4² + 2²

• Base = p/2 = 4/2 = 2cm

→ h² = 16 - 4

→ h² = 12

→ √h² = √12

→ h = 2√3

∴ Hence, Height of the equilateral triangle is 2√3.

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More to know:

• Area of triangle = ½ × base × height

• Heron's Formula = √s(s - a)(s - b)(s - c)

• Sum of all angles of a triangle is 180°.

Answer 2

Given -

• ABC is an equilateral triangle with side 4cm.

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To find -

• Height of the triangle.

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Solution -

• Let the height of the triangle be h.

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We know that, height of a equilateral triangle bisects the base.

Therefore,

• BD = DC = 2cm

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In triangle ADC

[By Pythagoras theorem]

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⠀• AC² = AD² + DC²

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→ (4)² = AD² + (2)²

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→ 16 = AD² + 4

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→ AD² = 16 - 4

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→ AD² = 12

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→ AD = √12

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→ AD = 2√3 cm

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Hence,

• Height of the given triangle is 2√3cm.

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