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