Question

find the side of an equilateral triangle whose area is 400✓3cm2​

Answer 1

Given :

• Area of an equilateral triangle = 400√3 cm²

To find :

• Side of an equilateral triangle

Knowledge required :-

• Formula of area of equilateral triangle :-

⠀Area of equilateral triangle = √3/4 a²

where,

• a is the side of the triangle

Solution :

⠀⠀⠀⇒ Area = √3/4 a²

⠀⠀⠀⇒ 400√3 = √3/4 a²

⠀⠀⠀⇒ 400√3 × 4/√3 = a²

⠀⠀⠀⇒ 400 × 4 = a²

⠀⠀⠀⇒ 1600 = a²

⠀⠀⠀⇒ √1600 = a

⠀⠀⠀⇒ ± 40 Reject - ve = a

⠀⠀⠀⇒ 40 = a

★ Side of equilateral triangle = 40 cm

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⠀⠀⠀⠀⠀⠀⠀⠀Verification :-

Substitute the value of a in 400√3 = √3/4 a²

LHS = 400√3

Taking RHS,

⠀⠀⠀⇒ √3/4 × (40)²

⠀⠀⠀⇒ √3/4 × 40 × 40

⠀⠀⠀⇒ √3 × 10 × 40

⠀⠀⠀⇒ 400√3

LHS = RHS

Hence, verified.

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⠀⠀⠀⠀⠀⠀Know MorE :-

• Perimeter of triangle = Sum of all its sides
• Area of Isosceles triangle = ½ × base × height
• Semi perimeter = (a + b +c )/2
• Heron's formula = √s(s - a)(s - b)(s - c)

where,

• a, b and c are the three sides of the triangle respectively.
• s is the semi - perimeter