Here is one way:
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These are {45°, 45°, 90°} triangles. There are 3 on the bottom row, and 1 on top. Actually, any four identical isosceles triangles would work.
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An isosceles triangle is defined as a triangle that has two sides of the same length. With two identical right triangles, it is possible to arrange them into a bigger triangle that has two sides that are the same length.
A rhombus can be split into 2 isosceles triangles or divided into 4 right angle triangles
Two isosceles right triangles, if joined hypotenuse-to-hypotenuse will make a square. Two squares, sided by side, make a rectangle which is a parallelogram, and not a square.
Make it a right triangle where one side of the right triangle is half the length of the non-identical side of the isosceles, the hypotenuse of the right triangle is the length of one of the identical sides of the isosceles triangle, then use the Pythagorean theorem. a^2+b^2=c^2. Where "a" is the length of one of the identical sides, and "c" is the length of half the non-identical sides. Solve for "b" and that is your height.
NOT POSSIBLEIt is not possible to put 20 isosceles triangles into the form of a square. It takes 2 isosceles triangles to make one square. 6 more isosceles triangles would have to be added before a larger square could be made.For an isosceles triangle with leg length x, the number of triangles needed to make a square is modeled by the equationN = 2 * x2where N is the number of triangles and x is the number of isosceles triangles touching any side of the square.There is no integer solution for x when N = 20, meaning it is not possible to arrange 20 isosceles triangles in the shape of a square.