Blank A = 60 units
Blank B = Triangle proportionality theorem
Blank C = 100 units
Solution:
Given DE || AC.
AD = 32, DB = 48, CE = 40
Let first find the measure of EB using triangle proportionality theorem.
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
[tex]$\frac{AD}{DB} =\frac{CE}{EB}[/tex]
[tex]$\frac{32}{48} =\frac{40}{EB}[/tex]
Do cross multiplication.
[tex]$ 32\times {EB} = 40 \times 48[/tex]
[tex]$ 32\times {EB} = 1920[/tex]
Divide by 32 on both sides of the equation.
EB = 60
Blank A = 60 units
Blank B = Triangle proportionality theorem
To find the measure of BC:
BC = CE + EB
= 40 + 60
= 100
BC = 100
Blank C = 100 units
