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Suppose a isosceles triangle of width w and height h is cut from a sheet of...

Suppose a isosceles triangle of width w and height h is cut from a sheet of plywood. And Alice starts to fly by it to the right with speed v. What Alice will say about the area of the triangle. What will she say is its circumference?

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Answer #1

Area of the isosceles triangle = 1/2 x w x h
Perimeter, P = w + 2a,                       ...(1)
Where a is the length of one of the equal sides.
Using Pythagoras theorem, (w/2)2 + h2 = a2
w2/4 + h2 = a2
4a2 = 4h2 + w2              [Multiplying with 4 on both the sides]
2a = SQRT[4h2 + w2]      [Taking square root on both sides]   
Substituting 2a in (1),
P = w + SQRT[4h2 + w2]

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