Question 1065705
Here you go, as step-by-step as I could think to make it:
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Larger leg: (x+3)
Hypotenuse: (x+6)
Smaller leg: x
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Pythagoras:
x^2 + (x+3)^2 = (x+6)^2
factor (x+3)^2 and (x+6)^2:
x^2+(x^2+6x+9) = (x^2+12x+36)
2x^2+6x+9 = x^2+12x+36
Move everything to the left side of the equation, adding/subtracting as the case may be:
2x^2-x^2+6x-12x+9-36 = 0 
Simplify:
x^2-6x-27 = 0
Factor the equation:
(x+3)(x-9) = 0
Split into two equations:
x+3 = 0 or x-9 = 0
x = -3 or x = 9
Since we are not looking for a negative number, let's discard the -3 and try the 9:
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Smaller leg = 9cm
Hypotenuse = 9+6 = 15
Larger leg = 9+3 = 12
If this is correct, we should be able to complete, per Pythagoras: a^2+b^2 = c^2
Let's see:
9^2+12^2 = 15^2
81+144 = 225 We have the correct answer.
:
John