Question

In DGE, DG = 8, GE = 17, and DE = 15. What is the length of DF? Round to the nearest hundred

Answer 1

7.06 units

Step-by-step explanation:

The given side lengths are indicated in the diagram below:

Using similar triangles, we have:

`\begin{gathered} (GF)/(8)=(8)/(17) \\ 17GF=64 \\ GF=(64)/(17) \\ GF=3.76 \end{gathered}`

Next, apply Pythagorean Theorem to triangle DGF.

`\begin{gathered} DG^2=DF^2+GF^2 \\ 8^2=DF^2+3.76^2 \\ DF^2=8^2-3.76^2 \\ DF^2=49.8624 \\ DF^{}=√(49.8624) \\ DF\approx7.06\text{ units} \end{gathered}`

The length of DF is approximately 7.06 units (to the nearest hundred).