macymack
Answered

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BD = 21 m.
BC= 25 m.
DE = 40 m.
AB = 7m.

Find AB


BD 21 M BC 25 M DE 40 M AB 7m Find AB class=

Sagot :

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.

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