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 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
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 Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product

 Pythagorean Theorem Space Diagonals In a rectangular prism, a space diagonal is a line that goes from a vertex of the prism, through the center of the prism to the opposite vertex. That line is also called triagonal or volume diagonal. A rectangular prism has 4 space diagonals. The Pythagorean theorem is useful when we need to find the length of a space diagonal in a rectangular prism. Let's see the following picture: c2=a2+b2 Find d. In order to find the value of d, we can use the following right triangle: d2=102+c2 In order to find the value of c, we can use this right triangle: Using the Pythagoran Theorem: c2 = 82+62 c2 = 100 c = 10 Going back to the first right triangle: d2=102+c2 d2=100+100 d2=200 d = in What is the longest object that will fit inside a 8-by-10-by-12 inch box? The longest object that will fit inside this box is a segment with the same length as the space diagonal. So we must find the length of the space diagonal of this box. In order to find the value of d, we can use the following right triangle: d2=122+c2 In order to find the value of c, we can use this right triangle: Using the Pythagoran Theorem: c2=102+82 c2=164 Going back to the first right triangle: d2=122+c2 d2=144+164 d2=308 d=17.6 in The longest object that will fit inside this box is a segment 17.6 in. long