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Answer:
Step-by-step explanation:
The given relations tell you the side lengths form an arithmetic sequence with a common difference of 2.
short side
long side = short side + 2
hypotenuse = long side + 2
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There is only one "Pythagorean triple" that is an arithmetic sequence. The reduced form is (3, 4, 5). The numbers in this triple have a common difference of 1, so your side lengths will be double these values:
shorter leg: 6 inches
longer leg: 8 inches
hypotenuse: 10 inches
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Alternate solution
As you can see, it is worthwhile to remember some Pythagorean triples. If you write an equation using the Pythagorean theorem, you can let s represent the short side.
s^2 +(s+2)^2 = (s+4)^2
2s^2 +4s +4 = s^2 +8s +16
s^2 -4s -12 = 0 . . . . . . . subtract (s^2 +8s +16) to put in standard form
(s -6)(s +2) = 0 . . . . . . factor
s = 6 or -2 . . . . . . . . . . values that make the factors zero
The only reasonable solution here is s=6.
The short side is 6", the longer side is 8", and the hypotenuse is 10".
