Answered

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A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.

Sagot :

sqdancefan

Answer:

  17 cm

Step-by-step explanation:

You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.

Pythagorean theorem

The relation between the side lengths in the right triangle is ...

  a² +b² = c²

Application

Substituting the given relations, we have ...

  a² +(2a-1)² = (2a+1)²

  a² +4a² -4a +1 = 4a² +4a +1

  a² -8a = 0 . . . . . . write in standard form

  a(a -8) = 0 . . . . . . factor

  a = 0 or a = 8

We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...

  c = 2(8) +1 = 17

The hypotenuse is 17 cm.

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Additional comment

You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.

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