Question

The area of an equilateral triangle is numerically to its perimeter. Find its paerimeter correct to 2 decimal places.

Answer 1

The answer is 20.79 units

Please refer the above photograph for the used process.

Let ABC be an equilateral triangle with sides 'a' units.

KEY POINTS TO REMEMBER :-

Perimeter of equilateral triangle is 3a (where 'a' is the side of he equilateral triangle)

By Heron's Formula, The area of an equilateral Triangle is equal to :-
$\frac{ \sqrt{3} }{4} {a}^{2}$

Where 'a' is the side of the equilateral triangle.


In the question, it is given that
Perimeter of equilateral triangle = area of equilateral triangle.

Decimal value of root3 is nearly equal to 1.732

Thanks!

Answer 2

$\fbox { Heya !! }$

Here is Your Answer

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Given :- Area of equilateral triangle = Perimeter

Area of equilateral∆ = √3 /4 a^2

$\fbox { perimeter of equilateral ∆ = 3a}$

According to the question

$\frac{ \sqrt{3} }{4} {a}^{2} = 3a \\ \\ \frac{ \sqrt{3} }{4} = \frac{3a}{ {a}^{2} } \\ \\ \frac{ \sqrt{3} }{4} = \frac{3}{a} \\ \\ \sqrt{3} a = 12 \\ \\ a = \frac{12}{ \sqrt{3} }$

Rationalising the denominator

$a = \frac{12}{ \sqrt{3} } \times \frac{ \sqrt{3} }{\sqrt{3} } \\ \\ \frac{12 \times \sqrt{3} }{3}$

Value of√3 = 1.732

$\frac{12 \times 1.732}{3} = \frac{20.784}{3} = 6.928$

Approx the value of a is " 6.92" cm

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QUESTION :- To find perimeter

perimeter = 3a

→ 3 × 6.92

→ 20.76

$\fbox { Answer :- 20.76 cm^2 }$

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Glad if Helped ..!!!