Answer:
Laura needs 78 inches border.
Step-by-step explanation:
From the given figure it is noticed that
\(\angle ABC=\angle DFG\) (Given)
\(\frac{AB}{BC}=\frac{3}{4}\)
\(\frac{DF}{FG}=\frac{18}{24}=\frac{3}{4}\)
\(\frac{AB}{BC}=\frac{DF}{FG}\)
Since two corresponding sides are proportional and a including angle is congruent, therefore the by SAS rule of similarity,
\(\triangle ABC\sim \triangle DFG\)
All corresponding sides of similar triangles are proportional.
\(\frac{3}{6}=\frac{18}{DG}\)
\(3\times DG=18\times 6\)
\(DG=36\)
Perimeter is the sum of all the sides. The perimeter of DFG is
\(S=18+24+36=78\)
Therefore Laura needs 78 inches border.
