Question 1133882
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
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