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Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AD=3AD=3 and AC=27,AC=27, what is the length of \overline{AB}?AB?

 Apr 8, 2022
 #1
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I'm trying to interpret your question:

 

right triangle(ABC) with right angle(B) and hypotenuse(AC).

 

BD is an altitude.

 

Since AC = 27 and AD = 3, DC = 24

 

Use this relationship:  AD / BD  =  BD / DC

                                      3 / BD  =  BD / 24

                                          BD2  =  72

                                            BD  =  sqrt( 72 )

 

triangle(ADB) with also be a right triangle with hypotenuse AB.

 

use the Pythagorean Theorem:  AD2 + BD2  =  AB2:

                 AB2  =  32 + ( sqrt(72) )2

                         .... 

 Apr 8, 2022

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