SOLUTION: A triangle ABC with ∠ABC = 90 has length of the side AB = 72 and length of BC = 54. What is the length of the perpendicular line from side AC to point B?

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Question 973973: A triangle ABC with ∠ABC = 90 has length of the side AB = 72 and length of BC = 54. What is the length of the perpendicular line from side AC to point B?
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
The hypotenuse, c, is sqrt(8100)=90
You draw the altitude, and that makes two triangles, each of which is similar to the original. I would draw all three triangles in the same way to show similarity and label them accordingly.
The whole hypotenuse is to the shorter leg, 54, as the shorter leg, 54, is to the shorter leg of the bisected hypotenuse.
(90/54)=(54/x)
2916=90x; x=32.4
(a/54)=(54/90) also works.
You don't have to solve for b, although it is easy enough.
a^2 +h^2=54^2
(32.4^2)+ h^2 = 2916
1049.76 +h^2 =2916
h^2=1866.24
h=43.2 units ANSWER
check with b
(43.2)^2 + 57.6^2=72^2
1866.24 + 3317.76= 5084





Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Let BD be the perpendicular line from side AC to point B.
By definition BD is the altitude drawn to the hypotenuse.




We use the theorem:

The altitude to the hypotenuse of a right triangle is the mean 
proportional between the segments into which it divides the hypotenuse. 

In other words,





Cross-multiply:





 

 

 

Edwin
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