Question

The area of an equilateral triangle is 81 under root 3 cm square. Its height is ​

Answer 1

Answer:

Area of equilateral triangle = 81√3 cm².

Formula : √3 s²/4 for equilateral triangle.

Hence, √3 s² /4 = 81√3

➸ √3 s² = 81 √3 * 4

➸ s² = 81 * 4

➸ s = √(81 * 4)

➸ s = √(9 * 9 * 2 * 2)

➸ side = 9 * 2

➸ side = 18 cm

Now, Finding the height :

Formula :- ½bh = 81√3

➸ ½ * 18 * h = 81√3

➸ 9 * h = 81√3

➸ height = 81√3/9

➸ height = 9√3 cm

CONCLUSION :-

• Area of the equilateral triangle = 81√3 cm².
• Side of the equilateral triangle = 18 cm.
• Height of the equilateral triangle = 9√3 cm.

Answer 2

$\rule{250}{2}$

✺ GIVEN ✺

Area of an equilateral triangle is 81√3 cm².

✺ TO CALCULATE ✺

The height of the equilateral triangle.

✺ ACKNOWLEDGEMENT ✺

✪ Area of an equilateral triangle :-

$\displaystyle{\sf{\frac{\sqrt{3}}{4}a^2 }}$

✪ Height of an equilateral triangle :-

$\displaystyle{\sf{\frac{\sqrt{3}a }{2} }}$

✺ SOLUTION ✺

A/q,

$\displaystyle{\sf{\frac{\sqrt{3}}{4}a^2 =81\sqrt{3} }}$

⇥ √3 cancels in both the sides.

$\displaystyle{\sf{\implies \frac{a^2}{4}=81 }}\\\\\displaystyle{\sf{\implies a^2=324 }}\\\\\displaystyle{\sf{\implies s=\sqrt{324} }}\\\\\boxed{\displaystyle{\sf{\implies a=18\ cm }}}$

➤ So, the side of the equilateral triangle = a = 18 cm.

We know,

Height of an equilateral triangle = $\displaystyle{\sf{\frac{\sqrt{3}a }{2} }}$.

Putting a = 18, we get :-

$\displaystyle{\sf{h=\frac{\sqrt{3}\times 18 }{2} }}$

$\displasytyle{\sf{\implies h=\sqrt{3}\times 9}}\\\\\underline{\boxed{\boxed{\displasytyle{\sf{\implies h=9\sqrt{3}\ cm}}}}}$

➛ So, the height of the given equilateral triangle is 9√3 cm.

$\rule{250}{2}$