SOLUTION: a triangle of largest size is inscribed in a Semi-circle. if the area of the triangle is 12.5 square metres , then find the radius of the semi-circle

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Question 907020: a triangle of largest size is inscribed in a Semi-circle. if the area of the triangle is 12.5 square metres , then find the radius of the semi-circle
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This triangle is half of a square shaped region (intuition from Geometry knowledge). The whole square region (if included both halves of the square) is 2%2A%2812.5%29=25 square meters. Also, the diameter of the semicircle is 2r, if r is the radius. The height of the triangle is r.

%281%2F2%29%282r%29%2Ar=12.5, using formula for area of a triangle. The triangle is isosceles, 45-45-90 type.

2r%5E2=25
r%5E2=12.5
highlight%28r=sqrt%2812.5%29%29