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3) In the accompanying diagram of right triangle ABC, CD is drawn perpendicular to hypotenuse AB
D
If AB = 16 and DB = 4, find BC. [Show all work.]
16

Respuesta :

calculista

Answer:

[tex]BC=8\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

Triangle ABC is similar to Triangle CBD by AA Similarity theorem

Remember that

If two triangles are similar, then the ratio of its corresponding sides is proportional

so

[tex]\frac{AB}{CB}=\frac{CB}{DB}[/tex]

[tex]CB^2=AB(DB)[/tex]

substitute the given values

[tex]CB^2=16(4)\\CB^2=64\\CB=8\ units[/tex]

Remember that

[tex]CB=BC[/tex]

therefore

[tex]BC=8\ units[/tex]

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