hypotenuse therom

"Find the length of a hypotenuse of a right triangle whose sides are x cm, (x+1)cm and (x+3)."

 

Using Pythagoras' theorem:

 

(x+3)² = (x+1)² + x²

 

x² + 6x + 9 = x² + 2x + 1 + x²

 

Collect terms:

 

x² - 4x - 8 = 0

 

Use the quadratic equation to find x = 2 + 2sqrt(3)  cm  (the other solution is negative, so can't be the length of a side of a triangle)

 

The hypotenuse is therefore x + 3  →  5 + 2sqrt(3) cm long

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