Ab is a base of the triangle and its vertex lies on a line parallel to base. Prove that of all these triangles perimeter is the least for isosceles triangle.
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beta study the book and sleep nicely n don't ask me if u don't know
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Answer:
Consider a right triangle and an isosceles triangle between two parallel line which are 8 units apart.
In the right triangle, AC = 82+82=82units∴perimeterofΔABC=8+8+82=27.31units
Similarly, for ΔDEF,DE=DF=82+42=45units.∴perimeterofΔDEF=45+45+8=8+85≅25.9units.
It is clear from the figure that the perimeter of the obtuse triangle is not the least.
Hence, the isosceles triangle will have the least perimeter.
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