Question

if the area of an equilateral triangle is 50√3 cm ^2 then find its altitude​

Answer 1

50√3 = √3* a²/4

a²= 200

a = 10√2

Answer 2

Answer:

5√6cm

Step-by-step explanation:

area of equilateral triangle =

$\frac{ \sqrt{3} }{4} {a}^{2}$

so,

$\frac{ \sqrt{3} }{4} {a}^{2} = 50 \sqrt{3} \\ \\ {a}^{2} = 50 \sqrt{3} \times \frac{4}{ \sqrt{3} } \\ \\ {a}^{2} = 200 \\ \\ a = 10 \sqrt{2} cm$

all the sides of equilateral triangle is equal

so, base = 10√2cm and height = h

area of triangle

$\frac{1}{2} \times base \times height$

$50 \sqrt{3} = \frac{1}{2} \times 10\sqrt{2} \times h \\ \\ h = \frac{50 \sqrt{3} \times 2}{10 \sqrt{2} } \\ \\ \frac{100 \sqrt{3} }{10 \sqrt{2} } \\ \\ \frac{10 \sqrt{3} }{ \sqrt{2} } \\ \\ \frac{5 \times \sqrt{2 } \times \sqrt{2} \times \sqrt{3} }{ \sqrt{2} } \\ \\ 5 \sqrt{6 } = h$