Math, asked by manjit0323p9kzbp, 1 year ago

if perimeter of equilateral traingle is 90 m ,find its area?

Answers

Answered by DaIncredible
11
We know that
Perimeter of equilateral triangle = 3a

90 cm = 3a

90 / 3 = a

a = 30 cm

Now,

We also know that
Area of equilateral triangle

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

Putting the value of a

 =  \frac{ \sqrt{3} }{4}  \times  {(30)}^{2}  \\  \\  =  \frac{ \sqrt{3} }{4}  \times 900 \\  \\  =   \sqrt{3}  \times 225 \\  \\  = 225 \sqrt{3}

We know that √3 = 1.732

 = 225 \times 1.732 \\  \\  = 389.7

So the area of equilateral triangle is 389.7 cm^2


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Answered by AhnaDey
4
Given ,
perimeter- 90 cm

Let x be the one side of a triangle

First ,
we find the one side of an equilateral triangle is
x+x+x = 90
=> 3x = 90
=> x = 90 ÷ 3
=> x = 30

Therefore , three sides are 30 [ equilateral triangle]
perimeter = 90 cm
Semiperemeter =
a + b + c\%2
= 30 + 30 + 30 % 2 = 45 cm

Now ,
we find the area of the triangle

Area=
 \sqrt{s(s - a)(s - b)(s - c)}
 \sqrt{45(45 - 30)(45 - 30)(45 - 30)}
 \sqrt{45 \times 15 \times 15 \times 15}
 \sqrt{3 \times 3 \times 5 \times 3 \times 5 \times 3 \times 5 \times 3 \times 5}
 \sqrt{ {3}^{2} } \times {3}^{2} \times {5}^{2} \times 3 \times 5
3 \times 3 \times 5 \times \sqrt{3 \times 5}
45 \sqrt{15}
45 \sqrt{15 {cm}^{2} }
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