Question

if the area of the equilateral triangle is 8√3 cm square find the perimeter​

Answer 1

Answer:

12*3cm

Step-by-step explanation:

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Answer 2

$\large{\underbrace{\underline{\sf{Understanding\;the\; Question}}}}$

Here in this question we have given area of an equilateral triangle and we have to find the perimeter of the triangle. To find the perimeter, first we have to find the length of each side of the triangle. Length of the side can be obtained by applying formula of area.

So let's start!

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GIVEN:-

→ Area of triangle=8√3cm²

TO FIND:-

→ Perimeter of the triangle

SOLUTION:-

We have formula for equilateral triangle:

$\underline{\boxed{\sf{Area\:of\: equilateral\:\triangle=\dfrac{\sqrt3}{4}\times Side^{2}}}}\star$

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put the value of area in the formula.

$\sf:\implies{8\sqrt3 cm^{2}=\dfrac{\sqrt3}{4}\times Side^{2}}$

$\sf:\implies{8\sqrt3 cm^{2}\times\dfrac{4}{\sqrt3}= Side^{2}}$

$\sf:\implies\cancel{{8\sqrt3 cm^{2}\times\dfrac{4}{\sqrt3}}= Side^{2}}$

$\sf:\implies{8\times 4 cm^{2}= Side^{2}}$

$\sf:\implies{32 cm^{2}= Side^{2}}$

$\sf:\implies{\sqrt{32 cm^{2}}= Side}$

Now we have to change 32 into it's prime factors.

$\sf:\implies{\sqrt{2\times 2\times 2\times 2 \times 2 cm^{2}}= Side}$

Now we can take pairs out, from under-root.

$\boxed{\sf:\implies{4\sqrt 2 cm= Side}}\;\star$

∵ The length of each side of equilateral triangle is 4√2cm.

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Now we have to find perimeter of equilateral ∆.

As each side of equilateral triangle is equal so it's formula will be:-

Perimeter of equilateral ∆=3×Side

Perimeter of equilateral ∆=3×4√2cm

Perimeter of equilateral ∆=12√2cm.

∵ So the required perimeter of triangle is 12√2cm.

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$\large\underbrace{\underline{\sf{More \:to\: know \:about \:triangles}}}}$

A triangle is a figure which has 3 sides

Property of triangle includes:-

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

• Sum of 2 sides of triangle must be greater than its third side.

Grouping of triangles:-

★ Equilateral triangle

→ A triangle which has all it's sides equal in length is called an equilateral triangle. Equilateral triangle also has all angles of equal measure.

★ Isosceles triangle

→ A triangle which has 2 sides of equal length is called an Isosceles triangle. Moreover 2 angles of Isosceles triangle are always equal.

★ Scalene triangle

→ A triangle which has neither it's side nor its angles equal is called a scalene triangle.

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