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To understand this problem first draw a representation of a right triangle. Label one leg x and the other leg x-2.
Given: the hypotenuse is 4 cm. more than the shorter leg so:
label the hypotenuse x-2+4 or x+2
Now use the Pythagorean Theorem to find the value of x
Order of operations says we have to multiply where possible so use the FOIL method.
combine like terms:
Move everything to the same side.
Subtract x^2 from both sides and you get:
Subtract 4x from both sides and you get:
Subtract 4 from both sides and you get:
Factor out an x and you get:
This statement is true when x=0 or (x-8)=0
add 8 to both sides and you get
x=0;x=8 However, because we are dealing with a length of a triangle x cannot=0
Therefore x=8 is the only answer to this problem.
Check your work!
your sides are 8;8-2;8-2+4 or 8;6;10
we know that
100=100 and therefore the answer checks out to be true.
Remember that you must always try to find a unit label for every answer. In this case it is centimeters so your final answer is 6 cm; 8 cm; and 10 cm
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