Question

find the perimeter of the triangle
If the area of equilateral triangle is 16V3.m​

Answer 1

Answer:

Step-by-step explanation:

Area of an equilateral triangle = 16✓3 cm²

✓3/4 × (Side)² = 16✓3

(Side)² = 16✓3×4/✓3

Side² = 64

Side = ✓64 = 8

Therefore,

Perimeter of an equilateral triangle = 3 × (Side) = 3 × 8 = 24 cm

Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• Perimeter of the equilateral $\triangle$ = 24 Cm

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• The area of equilateral triangle is 16√3 Cm².

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• Perimeter of the equilateral triangle = ?

$\bf{\underline{\underline \blue{Explanation:-}}}$

$\sf\underline{\red{\:\:\: Formula\:used\: here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Area = \frac{\sqrt{3} }{4} \times Side^2}$

$\sf\underline{\red{\:\:\: Now,Putting\:the\: values:-\:\:\:}}$

$\longrightarrow \sf {16\sqrt{3} = \frac{\sqrt{3} }{4} \times (a)^2}$

$\longrightarrow \sf {16\sqrt{3} \times 4 = \sqrt{3} \times a^2}$

$\longrightarrow \sf {64\sqrt{3} = \sqrt{3} \times a^2}$

$\longrightarrow \sf {64 = a^2}$

$\longrightarrow \sf {\sqrt{64} = a}$

$\longrightarrow \sf {a = 8 \: Cm}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

• The area of equilateral $\triangle$ = 8 Cm

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

$\sf\underline{\red{\:\:\: Again,Formula\:used\: here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Perimeter\:of\:\triangle = 3 \times Side}$

$\sf\underline{\red{\:\:\: Now,Putting\:the\: values:-\:\:\:}}$

$\longrightarrow \sf {Perimeter\:of\:the\:\triangle = 3 \times 8}$

$\longrightarrow \sf {Perimeter\:of\:the\:\triangle = 24\:Cm}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

• Perimeter of the equilateral $\triangle$ = 24 Cm

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$