elrd23
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What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale.


Any help is appreciated, thank you!

What is the length of the altitude drawn to the hypotenuse The figure is not drawn to scale Any help is appreciated thank you class=

Respuesta :

gorraricardezju
Hello!

Well, the altitude of a right triangle = sqrt of the two lengths it divides the hypotenuse into so in your problem, the altitude = sqrt of 5(14).

the 2 triangles ACD and ABC are similar (same shape - corresponding angles are equal) the property of similar triangles is that corresponding sides are in the same ratio.

Hope this all Helps! :)
boffeemadrid

Answer:

Step-by-step explanation:

Consider the figure, in Triangle ABC and triangle BDC, we have

∠ABC=∠BDC (90°)

∠C=∠C (reflexive)

Thus, by AA similarity rule, ΔABC is similar to ΔBDC.

Therefore, using the similarity condition,

[tex]\frac{AD}{BD}=\frac{BD}{DC}[/tex]

[tex](DB)^2=14{\times}5[/tex]

[tex](DB)^2=70[/tex]

[tex]DB=\sqrt{70}[/tex]

Thus, the length of the altitude= [tex]\sqrt{70}[/tex]

Ver imagen boffeemadrid

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