In triangle A, the longer leg is 4 more than the shorter leg, and the hypotenuse is 4 more then the longer leg. How do you find the short leg, the long leg, and the hypotenuse. x = shorter leg x + 4 = longer leg x + 8 = hypotenuse {it is 4 more than longer leg} a² + b² = c² {pythagorean theorem} x² + (x + 4)² = (x + 8)² {substituted into pythagorean theorem} x² + x² + 8x + 16 = x² + 16x + 64 {used foil method} 2x² + 8x + 16 = x² + 16x + 64 {combined like terms} x²  8x  48 = 0 {subtracted x², 16x, and 64 from both sides} (x  12)(x + 4) = 0 {factored into two binomials} x  12 = 0 or x + 4 = 0 {set each factor equal to 0} x = 12 or x = 4 {solved each equation for x} x = 12 {length of a side cannot be negative} x + 4 = 16 {substituted 16, in for x, into x + 4} x + 8 = 20 {substituted 12, in for x, into x + 8} short leg = 12 long leg = 16 hypotenuse = 20 © Algebra House
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