Question 239336: Area of the largest triangle that can be inscribed in a semi-circle of radius r units is
(A) r^2 sq. units b) 1/2 r^2 sq. units c) 2 r^2 sq. units
d)square root(2) r2 sq. units
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I believe the solution is going to be A (r^2 squared units).
The area of a triangle is equal to the base times the height.
In a semi circle, the diameter is the base of the semi-circle.
This is equal to 2*r (r = the radius)
If the triangle is an isosceles triangle with an angle of 45 degrees at each end, then the height of the triangle is also a radius of the circle.
A = (1/2)*b*h formula for the area of a triangle becomes:
A = (1/2)*2*r*r because:
The base of the triangle is equal to 2*r
The height of the triangle is equal to r
A = (1/2)*2*r*r becomes:
A = r^2
Since the area of the triangle is equal to (1/2)*b*h, and the base remains the same while the height of the triangle is less at any other point on the surface of the semi-circle, then the largest area is when the height equals the radius of the triangle.
Your answer is selection A.
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