johns0511
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Solve Similar Triangles (advanced)

Solve for X.

Solve Similar Triangles Advanced Solve For X class=

Sagot :

Given:

[tex]m\angle B=90^\circ, m\angle D=90^\circ, AB=6, BD=4, BC=2, DE=x[/tex].

To find:

The value of x.

Solution:

In triangles ABC and ADE,

[tex]\angle B\cong \angle D[/tex]              (Right angles)

[tex]\angle A\cong \angle A[/tex]              (Common angles)

[tex]\Delta ABC\sim \Delta ADE[/tex]              (AA property of similarity)

We know that the corresponding sides of similar triangles are proportional. So,

[tex]\dfrac{AB}{AD}=\dfrac{BC}{DE}[/tex]

[tex]\dfrac{6}{(6+4)}=\dfrac{2}{x}[/tex]

[tex]\dfrac{6}{10}=\dfrac{2}{x}[/tex]

[tex]\dfrac{3}{5}=\dfrac{2}{x}[/tex]

On cross multiplication, we get

[tex]3\times x=5\times 2[/tex]

[tex]3x=10[/tex]

[tex]x=\dfrac{10}{3}[/tex]

Therefore, the value of x is [tex]\dfrac{10}{3}[/tex] units.

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