When given the area and two sides of a triangle use Heron's Formula which states.

where a, b and c are the three sides of the triangle.

Call a=60cm, b=63cm and c the unknown side.

Let's try to simplify that right side before substituting what we know for a and b.

Multiply both sides by 16 to remove the denominator on the right. That makes the equation:

Substitute the values we know:

Set and rewrite the equation.

Subtract 20575296 from both sides.

Multiply both sides by -1.

Maybe the Rain Man could factor that, but we'll have to use the quadratic equation to find x, then take the square root of x to find c.

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=

=

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That gives and

and

So and

Both will work. To prove it, plug into another version of Heron's Formula which is:

Where a, b and c are the sides, and s is the semiperimeter and

For c=116.69 this is:

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For c=39 this is:

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