+62 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.
+129852 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
