One leg of a right triangle is 2 inches longer than the shorter leg. The hypotenuse is 4 inches longer than the shorter leg,
Find the lengths of the three sides of the right triangle.
Shorter leg -
inches
Longer leg -
inches
Hypotenuse -
inches
Enter NUMBER Only

9514 1404 393

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

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".

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