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

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