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Use the Pythagorean theorem to find the lengths of the sides of the right triangle.
Use a calculator when necessary.
5m
3m
2m+2

Sagot :

sqdancefan

9514 1404 393

Answer:

  in the order (5m, 3m, 2m+2), ...

  • 5, 3, 4
  • (2+√34)/3, (2+√34)/5, (34+2√34)/15 ≈ (2.6103, 1.5662, 3.0441)

Step-by-step explanation:

There are two possible solutions:

5m is the hypotenuse

  (5m)² = (3m)² +(2m+2)²

  25m² = 9m² +4m² +8m +4

  3m² -2m -1 = 0 . . . . . . . . . . . write in standard form, divide by 4

  (m -1)(3m +1) = 0 . . . . . . . . factor

The positive solution for m is the value that makes m-1=0. It is m=1.

The side lengths are ...

  5m = 5 . . . hypotenuse

  3m = 3

  2m+2 = 4

__

2m+2 is the hypotenuse

  (2m+2)² = (5m)² +(3m)²

  15m² -4m -2 = 0 . . . . . . . write in standard form, divide by 2

Then the solutions using the quadratic formula are ...

  m = (-(-4) ± √((-4)² -4(15)(-2)))/(2(15)) = (4 ± √136)/30 = (2±√34)/15

The positive solution for m is ...

  m = (2+√34)/15 ≈ 0.522063

Then the side lengths of the triangle are ...

  (2m +2) = (34 +2√34)/15 ≈ 3.0441 . . . hypotenuse

  5m = (2 +√34)/3 ≈ 2.6103

  3m = (2 +√34)/5 ≈ 1.5662

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