Question 1133882: Find the lengths of the sides of the right triangle. x, x+7, 2x+1.
Answer by algebrahouse.com(1659)   (Show Source):
You can put this solution on YOUR website! 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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