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Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse ACAC. If AC=20AC=20 and DC=5,DC=5, what is the length of \overline{BC}?BC? (Note: the figure is not drawn to scale.)

 Mar 18, 2021
 #1
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AC - DC  = AD

 

20  - 5  =   15

 

AD  / BD =  BD / CD

 

15  / BD  = BD  / 5

 

15 * 5  = BD^2

 

75  = BD^2

 

AC^2 =  BD^2  + CD^2

 

AC^2  =  75  + 5^2

 

AC^2  =  75  + 25

 

AC^2  =100

 

AC  = 10

 

cool cool cool

 Mar 18, 2021

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