Question

HELP. Last one. Confused...

Laura is making two art pieces that are both in the shape of triangles. She wants to glue a decorative border around the triangles.

How much border would she need for the ​ triangle DFG ​ ?


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Answer 1

I'm pretty sure it's 78 in.

Answer 2

Laura needs 78 inches border.

Explanation:

From the given figure it is noticed that

`\angle ABC=\angle DFG` (Given)

`(AB)/(BC)=(3)/(4)`

`(DF)/(FG)=(18)/(24)=(3)/(4)`

`(AB)/(BC)=(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.

`(3)/(6)=(18)/(DG)`

`3* DG=18* 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.