Question

Find the height of equilateral triangle whose side is 15 cm​

Answer 1

ANSWER :-

$area \: \: of \: \: triangle = \frac{ \sqrt{3 } {a}^{2} }{4} \\ \\ = \frac{ \sqrt{3} }{4} \times 15 \times 15 \\ \\ = \frac{225 \sqrt{3} }{4} \\ \\ we \: \: know \: \: the \: \: area \: of \: \: triangle \: \: \\ \\ = \frac{1}{2} \times b \times h \\ \\ \frac{225 \sqrt{3} }{4} = \frac{1}{2} \times 15 \times h \\ \\ h = \frac{225 \sqrt{3} }{4} \times 2 \times \frac{1}{15} \\ \\ h = \frac{15 \sqrt{3} }{4} \\ \\ h = 7.5 \sqrt{3}$

Answer 2

Answer:

height~ 13cm

Explanation:

divide the triangle into equal Half's using a median which is also the height of the triangle.

then in a triangle,

using pythogoras theorem,

${15}^{2} = {x}^{2} + {7.5 }^{2} \\ 225 = {x }^{2} + 56.25 \\ {x}^{2} = 168.75 \\ x = 12.99$

where X=height