Question

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

• A. $173.2c{m}^2;11.32$
• B. $173.2c{m}^2;19.32$
• C. $173.2c{m}^2;17.32$
• D. $173.2c{m}^2;14.32$

Answer 1

Answer: (C)

$173.2c{m}^2;17.32$

Given, perimeter of equilateral triangle is $60cm$.
Perimeter of equilateral triangle$=60cm$
3$\times$ side $=60$
$\therefore$ side $=\frac{60}{3}=20cm$.
Area of equilateral triangle $=\frac{\sqrt{3}{\left(side\right)}^2}{4}=\frac{\sqrt{3}\times {20}^2}{4}=100\sqrt{3}{cm}^2=173{.2cm}^2$
Height of equilateral triangle $=\frac{\sqrt{3}\left(side\right)}{2}=\frac{\sqrt{3}\times 20}{2}=10\sqrt{3}cm=17.32cm$