5. If the area of an equilateral triangle is 16√3 cm²?, find its perimeter. .​

Question

5. If the area of an equilateral triangle is 16√3 cm²?, find its perimeter. .​

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Jade 1 month 2021-08-12T06:47:52+00:00 2 Answers 0 views 0

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    0
    2021-08-12T06:49:24+00:00

    Given ,

    Area of an equilateral ∆ = 16√3 cm²

    We know that , the area of equilateral ∆ is given by

     \boxed{ \tt{Area =  \frac{ \sqrt{3} }{4} {(a)}^{2}  }}

    Where , a = side of equilateral ∆

    Thus ,

    16✓3 = ✓3/4 × (a)²

    16 = 1/4 × (a)²

    (a)² = 64

    a = ± 8 cm

    Since , the length can’t be negative

    Therefore , the side of equilateral ∆ is 8 cm

    Now , the perimeter of equilateral ∆ is given by

     \boxed{ \tt{Perimeter = 3a}}

    Thus ,

    Perimeter = 3 × 8

    Perimeter = 24 cm

    Therefore , the perimeter of equilateral ∆ is 24 cm

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    0
    2021-08-12T06:49:42+00:00

    Given :

    • Area of an equilateral triangle = 16√3 cm²

    To find :

    • perimeter

    Formula used :

    • Area of Equilateral Triangle (A) = (√3/4) a²
    • perimeter of Equilateral Triangle (A)= 3a

    where a = side of Equilateral Triangle

    Solution :

    Area of Equilateral Triangle (A) = (√3/4) a²

    16√3 = (√3/4) a²

    or

    (√3/4) a² = 16√3

    a² = 16√3 × 4/√3

    a² = 16√3 × 4/√3

    a = √( 16√3 × 4/√3)

    a = √3 × 2 × 4

    a = 8 √3 cm

    perimeter = 3a

    perimeter = 3 × 8 √3

    perimeter = 24√3

    Answer :

    perimeter = 24√3 cm

    ________________________

    Perimeter = sum of all sides

    Perimeter of rectangle = 2( length + breadth )

    Perimeter of square = 4 × a

    Circumference = 2πr

    Volume of cylinder = πr²h

    T.S.A of cylinder = 2πrh + 2πr²

    Volume of cone = ⅓ πr²h

    C.S.A of cone = πrl

    T.S.A of cone = πrl + πr²

    Volume of cuboid = l × b × h

    C.S.A of cuboid = 2(l + b)h

    T.S.A of cuboid = 2(lb + bh + lh)

    C.S.A of cube = 4a²

    T.S.A of cube = 6a²

    Volume of cube = a³

    Volume of sphere = 4/3πr³

    Surface area of sphere = 4πr²

    Volume of hemisphere = ⅔ πr³

    C.S.A of hemisphere = 2πr²

    T.S.A of hemisphere = 3πr²

    _______________________

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