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△ABC is a right triangle and line segment AD is an altitude.
If AB = 10 and BD = 8 then what is the area of \△ABC?

 

 Dec 4, 2019
 #1
avatar+11146 
+3

△ABC is a right triangle and line segment AD is an altitude.
If AB = 10 and BD = 8 then what is the area of \△ABC?

laugh

 Dec 4, 2019
 #2
avatar+106539 
+1

Note that triangle ABD  is a 6-8-10  Pythagorean Triple Right Triangle

 

And triangle ABD  is similar to triangle CDA...so

 

AD / BD  = CA / DA    ....so....

 

10/ 8   =  CA /  6      multiply both sides by  6

 

60 / 8   =  CA   =  7.5

 

So.....the area of ABC   = (1/2) (AB) (AC)  =  (1/2)(10(7.5)  =  37.5 units^2

 

 

 

cool cool cool

 Dec 4, 2019

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