SOLUTION: Please help me to find the answer. Find the length of a side of an equilateral triangle whose altitude is 3 feet shorter than a side.

Question 843443: Please help me to find the answer. Find the length of a side of an equilateral triangle whose altitude is 3 feet shorter than a side.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Set s = length of a side.
Bisecting one of the angles produces two triangles,
each with a base of (1/2)s. Since the height is 3
less than a side length, height = s - 3
By Pythagorean theorem

multiply each side by 4

subtract 4s^2 from each side

There are two possible values for s.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=432 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 22.3923048454133, 1.60769515458674. Here's your graph:

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