Question

fine length of side and perimeter of an equilateral triangle whose height is 5√3 cm​

Answer 1

Given :-

• a equilateral triangle AB = BC = AC
• height (altitude) of equilateral triangle = 5√3 cm

To find :-

1. lenght of equilateral triangle.
2. perimeter of the the triangle .

formula used :-

$\sf \: height \: of \: equilateral \: triangle = a \dfrac{ \sqrt{3} }{2}$

Solution :-

$\sf \: height \: = 5 \sqrt{3} \: cm \\ \\ \sf \: \therefore \: \: 5 \sqrt{3} \: = a \times \dfrac{ \sqrt{3} }{2} \\ \\ \sf \: (cross \: multiplication \: ) \\ \\ \implies \sf10 \sqrt{3} = a \sqrt{3} \\ \\\implies \therefore \sf \: \: a = \dfrac{10 \sqrt{3} }{ \sqrt{3} } \\ \\ \implies \bf a \: = 10 \: cm \:$

now we have side of equilateral triangle

side = 10 cm

perimeter of equilateral triangle = 3a

$\implies \sf \: 3a = \: 3 \times 10 \\ \implies \bf \:30 \: cm$

hence, perimeter = 30cm

• side of equilateral triangle = 10 cm
• perimeter of equilateral triangle = 30 cm