Question

The area of a equilateral triangle is 4√3 cm
then find the height of the triangle?​

Answer 1

CORRECT QUESTION :-

★ The area of an equilateral triangle is 4√3 cm². Find the length of each side of equilateral triangle.

GIVEN :-

• The area of an equilateral triangle is 4√3 cm².

TO FIND :-

• The length of each side of equilateral triangle.

SOLUTION :-

As we know that,

★ Area of equilateral triangle (A) = √3/4 a²

• A → Area of triangle.
• a → side of equilateral triangle.

→ 4√3 = √3/4 a²

→ a² = √3/4 × 4√3

→ a² = √3/16√3

→ a² = 16

→ a = √16

→ a = 4 cm.

As we know that in equilateral triangle all the sides are equal.

Hence each side of equilateral triangle measures 4 cm.

Answer 2

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❅CORRECT QUESTION:-

➟ Find the length of the each side of equilateral triangle whose area is 4√3 cm².

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❅ANSWER:-

➣GIVEN:-

• Area of equilateral triangle = 4√3 cm²

➣FIND:-

• Length of each side = ?

➣SOLUTION:-

→ we have,

⇨area of equilateral triangle = 4√3 cm²

→ we know that,

$\bold{⇨area \: of \: triangle = \frac{ \sqrt{3} }{4} {(side)}^{2} }$

now,

$\bold{⇨4 \sqrt{3} = \frac{ \sqrt{3} }{4} {(side)}^{2} }$

$\bold{⇨ \frac{4 \sqrt{3} \times 4 }{ \sqrt{3} } = {(side)}^{2} }$

$\bold{⇨ \frac{4 \cancel{\sqrt{3}} \times 4 }{ \cancel{\sqrt{3}} } = {(side)}^{2} }$

$\bold{⇨4 \times 4 = {(side)}^{2} }$

$\bold{⇨16 = {(side)}^{2} }$

now, we can also write 16 as 4²

$\bold{⇨ {4}^{2} = {(side)}^{2} }$

$\bold{⇨ {4 }\not{ ^{2}} = {(side)} \not{^{2}} }$

$\bold{⇨side = 4cm }$

$\bold{☄Hence, the \: length \: of \: each \: side \: of</strong><strong>}</strong><strong> \</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>l</strong><strong>d</strong><strong>{</strong><strong>euilateral</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>triangle</strong><strong> \: is \underline{\boxed{ \bold{4cm.}}}}$

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