Question

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

Answer 1

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

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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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Answer 2

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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