Triangles ABC and DFG are given. Find the lengths of all other sides of these triangles if:

Chapter Reference

b

∠A≅∠D, AB·DG=AC·DF, AC=7 cm, BC=15 cm, FG=20 cm, and DF-AB=3 cm

I found that AB is 9, and that DC is 12, but can't find AC or DG because there aren't that many clues that lead to the answer.

TwentyFour Feb 2, 2019

#1**+1 **

AB / BC = DF / FG

AB / 15 = (AB + 3)/20 (cross-multiply)

20AB = 15(AB + 3)

20AB = 15AB + 45

5AB = 45

AB = 9

DF - AB = 3 which implies that

Then DF = AB + 3 = 12

And we know that

AB * DG = AC * DF

9 * DG = 7 * 12

9* DG = 84

DG = 84/9 = 28/ 3

So AB = 9 AC = 7 BC = 15

And

DF = 12 DG = 28/3 FG = 20

Note that this is true.....the scale factor from ABC to DFG = 4/3

CPhill Feb 2, 2019