Given:
The diagram shows two right-angled triangles OAB and OCD.
To find:
The length of BD.
Solution:
Let the length of BD is x.
In triangle OAB and OCD,
[tex]\angle AOB\cong \angle COD[/tex] (Common angle)
[tex]\angle ABO\cong \angle CDO[/tex] (Right angle)
[tex]\Delta OAB\sim OCD[/tex] (By AA property of similarity)
We know that, the corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{AB}{CD}=\dfrac{OB}{OD}[/tex]
[tex]\dfrac{4}{7}=\dfrac{14}{14+x}[/tex]
[tex]4(14+x)=14(7)[/tex]
[tex]56+4x=98[/tex]
Subtracting 56 from both sides, we get
[tex]4x=98-56[/tex]
[tex]4x=42[/tex]
[tex]x=\dfrac{42}{4}[/tex]
[tex]x=10.5[/tex]
Therefore, the length of BD is 10.5 cm.
