SOLUTION: Please help me with this question: An artist used silver wire to make a triangle that has a perimeter of 30 inches. Shen then used copper wire to make the largest circle that could

Question 855606: Please help me with this question: An artist used silver wire to make a triangle that has a perimeter of 30 inches. Shen then used copper wire to make the largest circle that could fit in the triangle.
how many more inches of silver wire did the artist use compared to copper wire?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The center of the circle inscribed in the triangle is the incenter, the point at the same distance from all 3 sides.
It can be found as the intersection of the angle bisectors (all 3 intersect there, but we can find the incenter by drawing any two of them).

If I were the artist my triangle would be an equilateral triangle.

An equilateral triangle with a perimeter of 30 inches would have a side length of 10 inches.
In an equilateral triangle, the height is times the length of the side.
In an equilateral triangle, connecting the incenter to the vertices splits the triangle into 3 congruent triangles.
They all have the same base as the equilateral triangle,
and of the area of the equilateral triangle.
As a consequence their heights are of the height of the equilateral triangle.
Those heights, measured perpendicular to the sides to the incenter are the radius of the inscribed circle.
In my triangle the side measures inches;
the height of the equilateral triangle is inches,
and the radius of the inscribed circle is .
The circumference of the circle would be
inches (rounding).
If the artist uses 30 inches of silver wire for the triangle,
and 18.14 inches of copper wire for the circle,
she used more inches of silver wire than of copper wire.
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