Find the lengths of the sides of a triangle, if the side lengths are represented as x, x + 7, and 2x + 1. Use the Pythagorean Theorem
a² + b² = c² a and b are the legs c is the hypotenuse {the longest side} x and x + 7 are the legs 2x + 1 is the hypotenuse x² + (x + 7)² = (2x + 1)² {substituted into Pythagorean Theorem} x² + x² + 14x + 49 = 4x² + 4x + 1 {squared the binomials} 2x² + 14x + 49 = 4x² + 4x + 1 {combined like terms} 2x²  10x  48 = 0 {subtracted 2x², 14x, and 49 from each side} 2(x²  5x  24) = 0 {factored 2 out of left side} x²  5x  24 = 0 {divided each side by 2} (x  8)(x + 3) = 0 {factored into two binomials} x  8 = 0 or x + 3 = 0 {set each factor equal to zero} x = 8 or x = 3 {solved each equation for x} the length of a side cannot be negative x = 8 x + 7 = 15 2x + 1 = 17 8, 15, and 17 are the lengths of the sides Ask Algebra House Comments are closed.

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