Given: "h" is the altitude of an equilateral triangle with side "c".

h = (√3)/2.

Find: "c"

Solution:

We an use the Pythagorean Theorem. Since the triangle is equilateral, we know that the altitude intersects the base at distance c/2 from the side. Thus, we can write

h

h

h

h = ((√3)/2)*c (take the positive square root of both sides)

h/((√3)/2) = c (divide both sides by (√3)/2)

h*(2/√3) = c (for now, "invert and multiply")

Now, we can put in the value we have for h:

((√3)/2)*(2/√3) = c (perform the substitution)

((√3)/√3)*(2/2) = c (rearrange the operands so you can see how this simplifies)

1 = c The side of the triangle has length = 1.

h = (√3)/2.

Find: "c"

Solution:

We an use the Pythagorean Theorem. Since the triangle is equilateral, we know that the altitude intersects the base at distance c/2 from the side. Thus, we can write

h

^{2}+ (c/2)^{2}= c^{2}(Pythagorean Theorem applied to equilateral triangle)h

^{2}+ c^{2}/4 = c^{2}(compute the denominator)h

^{2}= c^{2}- c^{2}/4 = (3/4)c^{2}(subtract the left side "c" term from both sides)h = ((√3)/2)*c (take the positive square root of both sides)

h/((√3)/2) = c (divide both sides by (√3)/2)

h*(2/√3) = c (for now, "invert and multiply")

Now, we can put in the value we have for h:

((√3)/2)*(2/√3) = c (perform the substitution)

((√3)/√3)*(2/2) = c (rearrange the operands so you can see how this simplifies)

1 = c The side of the triangle has length = 1.