Question

The area of an equilateral triangle is 75root 3.Find the length of the altitude​

Answer 1

Answer:

root300 is the answer

Step-by-step explanation:

75root3=root3÷4×a×a

75root3×4÷root3=a×a

root3 and root3 gets cancel

75×4=a×a

300=a^2

√300=a

Answer 2

Answer:

h = 15

Step-by-step explanation:

$Given\: the \:area \:of\:an\\equilateral \: triangle (A)=75\sqrt{3}$

$Let \: length \:of \:the \\altitude=h$

$Let \:the \: length \:of \:the \:side = a$

$A = 75\sqrt{3}$

$\implies \frac{\sqrt{3}}{4} a^{2}=75\sqrt{3}$

$\implies a^{2}=75\sqrt{3}\times \frac{4}{\sqrt{3}}$

$\implies a^{2}=75\times 4$

$\implies a = 10\sqrt{3}$

$\implies h = \frac{\sqrt{3}}{2} a$

$=\frac{\sqrt{3}}{2} \times 10\sqrt{3}$

$=15$

Therefore,

h = 15

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