SOLUTION: 20 triangles measuring 3 x 6 assemble into a square

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 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Triangles Question 120044: 20 triangles measuring 3 x 6 assemble into a squareFound 2 solutions by checkley71, Edwin McCravy:Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!TRIANGLES 3X6 DON'T PROPERLY DESCRIBE TRIANGLES. BELIEVE YOU NEED ANOTHER MEASUREMENT. Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!Solution by Edwin: 20 triangles measuring 3 x 6 assemble into a square ``` 20 RIGHT triangles with legs measuring 3 and 6 can be assembled into a square this way. Let's calculate the length of the hypotenuse of each of those right triangles using the Pythagorean theorem. c² = a² + b² c² = 3² + 6² c² = 9 + 36 c² = 45 c = c = c = Each of the 20 right triangle has an area calculated by A = bh = (3)(6) = 9 square units The area of the square must be 20 times as much as the area of one triangle, or 9x20 or 180 square units. We can now calculate the side of the square by using the formula for the area of a square, A = 180 = Taking square roots of both sides, = = = Therefore each side of the square, being , is twice the hypotenuse of each triangle, which is . Let's draw that square: So we place two triangles on each side, 8 triangles in all, with their hypotenuses along the side of a square like this: Then draw 4 more line segments, making a smaller square in the middle of the big square, and 4 rectangles around it like this: Notice that the square in the middle is a 6x6 square and the 4 rectangles around it are 3x6 rectangles. Now we can split the 6x6 square into 2 3x6 rectangles, like this: Now we have 6 3x6 rectangles each of which can be split into 2 right triangles with legs 3 and 6, by drawing in a diagonal of each, like this: That's it! Count the rectangles. They're 20 of them. Edwin```