Geometry: area of equil. triangle numerically equal to length of one side

Merp

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The area of an equilateral triangle is numerically equal to the length of one of its sides. What is the perimeter of the triangle, in units? Express your answer in simplest radical form.

Here was my approach:

I drew a equilateral triangle and labeled x as the altitude and y as one of the side. I put (xy)/2=y
This gave me y=0, but thats impossible. Help anyone?

 
The area of an equilateral triangle is numerically equal to the length of one of its sides. What is the perimeter of the triangle, in units? Express your answer in simplest radical form.

I drew [an] equilateral triangle and labeled x as the altitude and y as one of its [sides]. I put (xy)/2=y
This gave me y=0, but [that's] impossible.
y=0 is one solution, but there's another.

Use the Pythagorean Theorem, to express x in terms of y.

Substitute this expression for x, in your equation xy/2=y. You'll end up with a quadratic equation. :cool:
 
The area of an equilateral triangle is numerically equal to the length of one of its sides. What is the perimeter of the triangle, in units?

I drew a equilateral triangle and labeled x as the altitude and y as one of the side. I put (xy)/2=y
This gave me y=0, but thats impossible.
It's not impossible; it's just trivial.

Now assume that y does NOT equal zero. This means that it's okay to divide through by y, which leaves you with... what?

Now that you have the numerical value of the height, you can apply the Pythagorean Theorem, as suggested, and solve for the value of y. ;-)
 
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