Question

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

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

To find:-

• Area of given triangle

According to Question:-

Let one side of triangle = x m

Triangle is equilateral!

★ All sides = x m

$\Rightarrow$ Perimeter = x + x + x

$\Rightarrow$ 3x = 60

$\Rightarrow$x = 60/3

$\Rightarrow$ x = 20

★Side of triangle = 20 m

Now,

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

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

━━━━━━━━━━━━━━━━━

The perimeter of an equilateral triangle is 60mt then the area is_mt?

A) 10√3

B) 15√3

C)20√3

$\rm\underline\bold{D)\:100✓3 \red{\huge{\checkmark}}}$