Question 1065705: The larger leg of a right triangle is 3 cm longer than its smaller leg. The hypotenuse is 6 cm longer than the smaller leg. How many cms long is the smaller leg? We understand how to square and take the square of the solution. We have no numbers with which to work more than x+3 for the longer leg and x=6 for the hypotenuse. We tried substitution. What is the answer?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! 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
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