The-perimeter-of-an-equilateral-triangle-is-24-Find-it-s-area-

Question Number 166715 by alephzero last updated on 26/Feb/22

The perimeter of an equilateral

triangle is 24 . Find {it}^{'} s area .

Answered by Rasheed.Sindhi last updated on 26/Feb/22

L e t e a c h o f s i d e s :

a = b = c = l

p e r i m e t e r = 3 l = 24

l = 8

\begin{matrix} s = \frac{a + b + c}{2}; ▴ = \sqrt{s (s - a) (s - b) (s - c)} \end{matrix}

s = \frac{3 l}{2}

▴ = \sqrt{\frac{3 l}{2} {(\frac{3 l}{2} - l)}^{3}} = \sqrt{\frac{3 l}{2} \cdot \frac{l^{3}}{2^{3}}} = \frac{l^{2}}{2^{2}} \sqrt{3}

= \frac{8^{2}}{4} \sqrt{3} = 16 \sqrt{3}

Commented by alephzero last updated on 26/Feb/22

{(\frac{3 l}{2} - l)}^{3} = \frac{l}{2} ?

Commented by Rasheed.Sindhi last updated on 26/Feb/22

S o r r y f o r m i s t a k e! h a v e c o r r e c t e d

n o w . T h a n k y o u!