What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.
Therefore, the area of the circle inscribed into this triangle is
The length of the sides of triangle are 3, 4, and 5.
We know that the largest ellipse that can be inscribed into any kind of triangle is a circle.
Same applies particularly for right triangles, as well.
We also know that,
For any kind of triangle with side lengths a,b, and c, if r is the radius of the circle inscribed into the triangle, and , then for the triangle's area applies , which leads to .
A triangle with side lengths 3, 4, and 5 is a right triangle, so we have
So, the area of the circle inscribed into this triangle is
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