Question

If D, B, equals, 20DB=20, B, C, equals, 16BC=16, D, C, equals, 12DC=12, E, F, equals, 28EF=28, and G, F, equals, 21GF=21, find the perimeter of triangle, E, F, G△EFG. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Answer 1

Notice triangle DBC has sides 12, 16, 20, so 12^2 + 16^2 = 144 + 256 = 400 = 20^2 — it is a 3-4-5 right triangle scaled by 4.

Compare sides:
- EF/BC = 28/16 = 7/4
- GF/DC = 21/12 = 7/4

So triangles DBC and EFG are similar with scale factor 7/4. The third side is
EG = DB*(7/4) = 20*(7/4) = 35.

Perimeter = EF + FG + GE = 28 + 21 + 35 = 84.

No rounding necessary.