Question

If the perimeter of an equilateral triangle is 90 m, then its area is ............. m2

Answer 1

Answer:

225✓3

Step-by-step explanation:

let side be x

x+x+x=90

3x=90

x=30m

area of equalateral triangle = (✓3a^2)/4

then, area = (✓3*30^2)/4

= 900✓3/4

=225✓3 m^2

Answer 2

Given :-

Perimeter the equilateral ∆ = 90 m

To Find :-

It's area

Solution :-

We know that,

Perimeter of equilateral ∆ = 3a

where, a is the measure of each side.

A/q,

90 m = 3a

$\implies\: a\: =\: {\dfrac{90}{3}}$

$\implies$a = 30

Therefore, length of each side is 30 m

Now,

Area of equilateral ∆

$A\: =\: {\dfrac{\sqrt3}{4}}\: a^2$

On inserting the values in the formula

We get ,

$A\: =\: {\dfrac{\sqrt3}{4}}\: 30^2$

$\implies\: A\: =\: {\dfrac{\sqrt3}{4}}\: 30 \times 30$

$\implies\: A\: =\: \sqrt3\: \times 15\: \times 15$

$\implies\: A\: =\: 225\sqrt3$

$\implies\: A\: =\: 225\: \times 1.732$

$\implies\: A\: =\: 389.7 m^2$

Therefore, area of the given triangle is 389.7 m²