SOLUTION: I need help with finding an equation for: A piece of wire is 5 feet long is to be cut into 2 pieces, one piece is X feet long and is bent into the shape of an equilateral triang

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Question 678994: I need help with finding an equation for:
A piece of wire is 5 feet long is to be cut into 2 pieces, one piece is X feet long and is bent into the shape of an equilateral triangle. the other piece is bent into a circle. Find an equation for the total area of the triangle and the circle as a function of X.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The whole length of wire is +5+ ft
+x+ ft is used for the equilateral triangle
+5+-+x+ is used for the circle
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The area of the triangle is A+=++%281%2F2%29%2Ab%2Ah+
The base is +x%2F3+ . The height is +%281%2F2%29%2A%28x%2F3%29%2Asqrt%283%29+
+A+=+%281%2F2%29%2A%28x%2F3%29%2A%28x%2F6%29%2Asqrt%283%29+
+A+=+%28+x%2Asqrt%283%29%29+%2F+36+
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The area of the circle is +pi%2Ar%5E2+
To find r, find the circumference
+C+=+2%2Api%2Ar+
+5+-+x+=+2%2Api%2Ar+
+r+=+%28+5+-+x+%29+%2F+%282%2Api%29+
and
+A+=+pi%2A%285+-+x%29%5E2+%2F+%28+4%2Api%5E2+%29+
+A+=+%281%2F%284%2Api%29%29%2A%28+25+-+10x+%2B+x%5E2+%29+
Hope I got it