Question

find the height of an equilateral triangle whose area is 49 * square root of 3

Answer 1

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

Area of an equilateral triangle=49√3 ....(Given)

$∴ \: \: \: \frac{ \sqrt{3} }{4} a^{2} = 49 \sqrt{3} \\ {a}^{2} = 49 \sqrt{3} \times \frac{4}{ \sqrt{3} } \\ {a}^{2} = 49 \times 4 \\ {a}^{2} = 196 \\ a =±14$

We know, side cannot be negative.

Therefore, side of triangle= 14

$Area\:of\:triangle = \frac{1}{2} \times base \times height \\ 49 \sqrt{3} = \frac{1}{2} \times 14 \times height \\ 49 \sqrt{3} = 7 \times height \\ \frac{49 \sqrt{3} }{7} = height \\ height = 7 \sqrt{3}$

Thus, height of an equilateral triangle=7√3 units.