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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=x, BD=9, BC=1, DE=5[/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{x}{x+9}=\dfrac{1}{5}[/tex]

On cross multiplication, we get

[tex]5x=x+9[/tex]

[tex]5x-x=9[/tex]

[tex]4x=9[/tex]

[tex]x=\dfrac{9}{4}[/tex]

[tex]x=2.25[/tex]

Therefore, the value of x is 2.25 units.

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