How Do You Divide A Square Root Fraction By A Square Root?


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Oddman answered
Given: "h" is the altitude of an equilateral triangle with side "c".
h = (√3)/2.

Find: "c"

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
h2 + (c/2)2 = c2    (Pythagorean Theorem applied to equilateral triangle)
h2 + c2/4 = c2    (compute the denominator)
h2 = c2 - c2/4 = (3/4)c2    (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.

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