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

Guest May 8, 2017

#1**+1 **

"*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} + x^{2}

x^{2} + 6x + 9 = x^{2} + 2x + 1 + x^{2}

Collect terms:

x^{2} - 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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Alan
May 9, 2017