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If the small triangles are worth 1, determine the value of the other Tangram pieces.

Be sure to explain your reasoning.

More Challenging Version:

Find the fractional part each tangram piece is of the whole (all 7 pieces).

Now, suppose the large triangles are worth 1/2, determine the value of the other Tangram pieces.

Be sure to explain your reasoning.

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Q: What is the fraction value of a medium triangle in a square?
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If a triangle has two side lengths of five and twelve what is the value of the third side?

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Can a triangle exist whose sum of two sides is equal to third side?

No. No Triangle exists where the sum of 2 sides of the triangle is either equal to the third side or is less than the third side.Even, if we consider Right-Angled Triangle, then according to Pythagoras Theorem, c2= a2+b2, where c=Hypotenuse, a and b are the other 2 sides of the triangle. Now, if we consider the minimum +ve value of a and b which is greater than 0, i.e, if we consider a = 1 unit and b = 1 unit, then the value ofc = square-root of (1^2 + 1^2) = square-root of (1 + 1 ) = square-root of (2) which is < than the sum of the value of side a and b. Since the value of square-root is additive in nature, for any +ve value of a and b, this result stands true.Hence, The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the the measure of the third side. This rule must be satisfied for all 3 permutations of the sides. In other words, as soon as you know that the sum of 2 sides is less than the measure of a third side, then you know that the sides do not make up a triangle .Regards,Suvarthi DasBirati, Kolkata-81