Question

If The perimeter of a equilateral triangle is 180cm then its area will be
​

Answer 1

c.900 root 3 cm²

Step-by-step explanation:

lenth of each side is 180/3=60cm.

then, area of equilateral triangle is

$\sqrt{3a {}^{2} } \div 4$

where a refers to side of triangle.....

$(\sqrt{3} \times {60}^{2} ) \div 4$

=900root 3(c)

Answer 2

Answer:

(b) $900\sqrt{3}cm^{2}$

Step-by-step explanation:

Given:-

Perimeter of the equilateral triangle $=180cm$

To find:-

Area of the equilateral triangle

Solution:-

Let side of the equilateral triangle be $a$

Perimeter of the equilateral triangle $=3a$

$180=3a$

$a=\frac{180}{3}$

$a=60cm$

Area of an equilateral triangle $=\frac{\sqrt{3}}{4}(a)^{2}$

⇒ $\frac{\sqrt{3}}{4}(60)^2$

⇒ $\frac{\sqrt{3}}{4}(60)(60)$

⇒ $\sqrt{3}(15)(60)$

⇒ $900\sqrt{3}cm^{2}$

∴ The area of the equilateral triangle $=$ (b) $900\sqrt{3}cm^{2}$.