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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.

 Feb 2, 2019
 #1
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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

 

 

cool cool cool

 Feb 2, 2019

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