Question

can anyone explain, in detail, the answer to this question? write the area "A" of an equilateral trinagle as a function of is side length x.

Answer 1

area = base*height /2

Answer 2

height = 2x sin(60) = sqrt(3)/2

base = 2x

Answer 3

area of the triangle = 1/2 * base * height
= 1/2 * x * height

Answer 4

we could just as easily go with sides of x

Answer 5

x*x*sqrt(3)
---------- = x^2 sqrt(3)/4
2*2

Answer 6

you can calculate the height using trigonometry:
tan 60 = height / (x/2)

Answer 7

so height = sqrt3 * 2 / x
now plug this into the formula for the area

Answer 8

somethings amiss there. there shouldnt be an "x" in the denominator that I can tell

Answer 9

tan(60) = sqrt(3)

sqrt(3) = 2h/x

x sqrt(3)
------- = h ; is better
2

Answer 10

if you keep x/2 in the denom; then you dont need to reciprocate it; you simply multiply by x/2

Answer 11

\[\sqrt{3}=\frac{h}{x/2}\]
\[\sqrt{3}(x/2)=\frac{h(x/2)}{x/2}\]
\[\sqrt{3}(x/2)=h\]
\[\frac{x\sqrt{3}}{2}=h\]