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

Ar of Δ = √s(s-a)(s-b)(s-c)

then S= 45/2 = then

√{45/2 (45/2 -15)^3} = √{45/2×(15/2)^3 } = √45/2 × 3375/8 = √9492.18 = 97.43 cm^2

or √3/4 ×15×15 = 225√3/4

then the height will be

using ar of Δ = 1/2 ×b×h = 225√3/4 Or 97.43

we get... h = 450√3/ 4×15 = 7.5 √3 answer....