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Answer :

Answer: 54 in.

Step-by-step explanation:  So, the problem does something a little sneaky, and that is they ask for the TOTAL amount of wood needed for triangle DFG.  And to find that, we simply have to multiply side AC by 3 to get side DG.  We do this because triangle ABC is 3 times as small as triangle DFG.   Then, add your side DG that you just got, (21) to side FG and FD to get the total amount of wood needed, 54 in.

The length of wood needed for triangle DFG is 54 inches

Start by calculating the side length DG in triangle DFG

The side lengths of DFG are three times the corresponding side length of ABC

So, we have:

[tex]DG = 3 \times AC[/tex]

[tex]DG = 3 \times 7\ in[/tex]

[tex]DG = 21\ in[/tex]

The perimeter of triangle DFG is then calculated as:

[tex]P = DF + FG + DG[/tex]

This gives

[tex]P = 15 + 18 + 21[/tex]

[tex]P = 54[/tex]

Hence, the length of wood needed is 54 inches

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