Question

29. The perimeter of an equilateral triangle is 60mt then the area is_mt?
A) 10√3
B) 15√3
C)20√3
D) 100√3​

Answer 1

$\huge{\underline{\underline{\tt{\pink{Answer}}}}}\:$

$\:\sf\underline\green{Given}\:$

The perimeter of an equilateral triangle is 60m

$\:\sf\underline\purple{To\:find}\:$

The area of the given triangle

$\:\sf\underline\orange{Concept\:insight}\:$

The perimeter of an equilateral triangle is 3 × length of side . The area of an equilateral triangle is $\sf\frac{\sqrt{3}}{4}$ × (Side)²

$\:\sf\underline\red{Solution}\:$

Let us take the measurement of each side of the triangle as x .

Now we know that the perimeter of the triangle would be ,

= 3 × x = 60

= 3x = 60

= x = $\sf\frac{60}{3}$

= x = 20 m

For finding the area , we have the formula as $\sf\frac{\sqrt{3}}{4}$ × (Side)²

Let's substitute the value of side as 20 m

We have ,

= $\sf\dfrac{\sqrt{3}}{4}$ × 20 × 20

= $\sf\dfrac{\sqrt{3}}{4}$ × 400

= $\sf\sqrt{3}$ × 100

= $\sf{100\:\times\:\sqrt{3}}$

Therefore , the answer is D) 100√3

Answer 2

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${\bf \underline{ Given}}\begin{cases} & \sf{Perimeter\:of\;the\:triangle\;is\: \bf{60\;m}} \\ & \sf{Given\;triangle\;is\;\bf{equilateral}} \end{cases}$

${ \bold { \underline{To\:Find : }}} \:$

• Area of given triangle

${ \bold { \underline{Solution : }}} \:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\large\underbrace{\underline{\sf{How\: to\: solve\: it\: :}}}$

Firstly, we will find the side of the triangle by putting values in the formula of the perimeter of triangle . Then, we will put value of it's side in formula of area of equilateral triangle.

So, let's start solving !!

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❂ Let one side of triangle = x m ❂

Triangle is equilateral!

∴ All sides = x m

➪ Perimeter = x + x + x

➪ 3x = 60

➪ x = 60/3

➪ x = 20

∴ Side of triangle = 20 m

Noω,

${\boxed {\boxed {\underline {\overline {\sf \bigstar \:Area_{(Equilateral\:triangle)}\leadsto\:\dfrac{\sqrt{3}}{4} \:\times\:(side)^2\:\bigstar\:\:}}}}}$

Putting all values :-

$\:\:\:\:\:\ratio\implies\:\sf{\dfrac{\sqrt{3}}{4} \:\times\:(20)^2}$

$\:\:\:\:\:\ratio\implies\:\sf{\dfrac{\sqrt{3}}{4} \:\times\:20\:\times\:20}$

$\:\:\:\:\:\ratio\implies\:\sf{\dfrac{\sqrt{3}}{\cancel{4}} \:\times\:{\cancel{20}\:\times\:20}}$

$\:\:\:\:\:\ratio\implies\:\sf{\sqrt{3} \:\times\:5\:\times\:20}$

$\:\:\:\:\:\ratio\implies\:\sf{\sqrt{3} \:\times\:100}$

$\:\:\:\:\:\ratio\implies\:\boxed{\boxed{\sf{100\sqrt{3} }}}\:\bigstar$

So, area of triangle = 100√3

$\underline{\boxed {\tt {\therefore {Option\:(D)\:100\sqrt{3}\:is\:correct}}}}\:\bigstar$

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