Respuesta :
Answer:
The measure of the side DE is [tex]\frac{7}{3}[/tex] unit .
Step-by-step explanation:
Given as Δ ABC and Δ ADE are similar :
The measure of side AB = 6 unit
The measure of side BD = 4 unit
The measure of side BC = 7 unit
Let The measure of side DE = x unit
From The property of similar triangle
[tex]\dfrac{\textrm The measure of side AB}{\textrm The measure of side AD}[/tex] = [tex]\dfrac{\textrm The measure of side BC}{\textrm The measure of side DE}[/tex]
or. [tex]\dfrac{\textrm 6}{\textrm AB - AD}[/tex] = [tex]\dfrac{\textrm 7}{\textrm x }[/tex]
or, . [tex]\dfrac{\textrm 6}{\textrm 6 - 4}[/tex] = [tex]\dfrac{\textrm 7}{\textrm x }[/tex]
Or, [tex]\dfrac{\textrm 6}{\textrm 2}[/tex] = [tex]\dfrac{\textrm 7}{\textrm x }[/tex]
or, 3 × x = 7
∴ x = [tex]\frac{7}{3}[/tex]
Hence the measure of the side DE is [tex]\frac{7}{3}[/tex] unit . answer
