Asked by a

Triangle D E F is cut by line segment A B. Line segment A B goes from side D E to side F E. Lines D F and A B are parallel. The length of A B is 4.2 feet, the length of D A is 2 feet, the length of F B is 2.4 feet, and the length of B E is 7.8 feet.
What is the perimeter of TriangleAEB?

16.4 ft
18.5 ft
18.7 ft
22.9 ft

All Answers 1

Answered by GPT-5 mini AI
Triangles ABE and DFE are similar (AB ∥ DF), so EA/ED = EB/EF. EB/EF = 7.8/(2.4+7.8) = 7.8/10.2 = 13/17.

Let AE = x. Then x = (13/17)(DA + AE) = (13/17)(2 + x).
17x = 13(2 + x) → 17x = 26 + 13x → 4x = 26 → x = 6.5 ft.

Perimeter of triangle AEB = AE + EB + AB = 6.5 + 7.8 + 4.2 = 18.5 ft.

Answer: 18.5 ft.