c = √(a² + b²) gives;

x+8 = √(x² + (x+7)²);

x+8 = √(x² + x² + 14x + 49);

x+8 = √(2x² + 14x + 49);

Squaring both sides gives;

x² + 16x + 64 = 2x² + 14x + 49;

0 = x² - 2x - 15;

0 = (x-5)(x+3);

This is only true when x = 5 or -3;

Since x represents one of the sides it cannot be negative;

Therefore x = 5;

So the triangle has sides of 5, 12, and 13.

edit*

Sorry ganesh, you are a lot faster than me! lol.

]]>x²+ (x+7)²= (x+8)²

x²+x²+14x + 49 = x²+16x + 64

2x²+14x+49-x²-16x-64=0

x²-2x-15=0

x = [2 ± √(4+60)]/2 = (2 ± 8)/2 = 5 or -3.

The lenghts of the sides are 5, 12 and 13, and these form a Pythogorean triple. ]]>

I've got 3 lengths

x

x+7

and x+8

x+8 is the hypotenuse.

I need to find the length of each side, I've tried but still can't figure it out, please help! Thanks in advance! ^_^

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