The three dotted lines are all parallel, this splits the large triangle into 3 similar right triangles. EFG, CDG, and ABG
Similar triangles have proportional sides.
Look at triangle EFG, you are given length of two of the sides.
EG = 0.75
GF = 1.5
The proportion is:
[tex]\frac{GF}{EG} = \frac{1.5}{.75} = \frac{2}{1} [/tex]
Now triangle CDG, we know CG = 1.75
To find side GD use the 2:1 proportion. It will be 2 times the smaller side.
[tex]\frac{GD}{CG} = \frac{GD}{1.75} = \frac{2}{1} \\ \\ GD = 2*1.75 = 3.5[/tex]
Do the same for triangle ABG
[tex]\frac{GB}{AG} = \frac{GB}{3.25} = \frac{2}{1} \\ \\ GB = 2*3.25 = 6.5 [/tex]
Find DB
[tex]DB = GB - GD = 6.5 - 3.5 = 3[/tex]
Area of Beets rectangle is:
2*3 = 6
