I need help.. with this

9514 1404 393

  7.06

Step-by-step explanation:

This triangle can be solved a couple of ways. In the end, they amount to the same thing.

1) The area is ...

  A = 1/2bh = 1/2(8)(15) = 60 . . . using DG as the base

Using GE as the base, the height (DF) is ...

  A = (1/2)(17)(DF)

  2(60)/17 = DF = 120/17

  DF ≈ 7.06

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2) Using similar triangles, we can find the ratio of the long side to the hypotenuse as ...

  (long side)/(hypotenuse) = DE/GE = DF/DG

  DF = DG(DE/GE) = 8(15/17) = 120/17

  DF ≈ 7.06