Given:
Let us consider the given sides are:
[tex]BD=21m[/tex]
[tex]BC=25m[/tex]
[tex]DE=40m[/tex]
[tex]AB=xm[/tex]
To find:
The length of side AB.
Solution:
Suppose the measure of AB be x.
From the given figure it is clear that,
[tex]\angle ADE \cong \angle ABC[/tex] (Right angles)
[tex]\angle ADE \cong \angle ABC[/tex] (Corresponding angles)
In triangles ABC and ADE, two corresponding angles are congruent. So, by AA property of similarity,
[tex]\Delta ABC\sim \Delta ADE[/tex]
We know that, corresponding sides of similar triangle are proportional.
[tex]\dfrac{AB}{BC}=\dfrac{AD}{DE}[/tex]
[tex]\dfrac{x}{25}=\dfrac{(x+21)}{40}[/tex]
[tex]40x=25(x+21)[/tex]
[tex]40x=25x+525[/tex]
Isolating the x terms, we get
[tex]40x-25x=525[/tex]
[tex]15x=525[/tex]
[tex]x=\dfrac{525}{15}[/tex]
[tex]x=35[/tex]
Hence, the measure of AB is 35 m.
