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In the right triangle, a height is drawn to the hypotenuse. Find x+y+z.

 

 Dec 29, 2020
 #1
avatar+836 
+2

x+y = sqrt(92 + 122) = 15

 

z = (9 * 12) / 15  = 7.2

 

x+y+z = 22.2 units

 Dec 29, 2020
 #5
avatar+836 
+2

The first row should be     x+y = sqrt(92 + 122) = 15

jugoslav  Dec 30, 2020
 #2
avatar+114171 
+1

We  have a   9 - 12  - 15  right triangle

 

So  x +  y =  15  =  base length of this triangle

 

The  area of this triangle  =(1/2) (9)(12)  =   (1/2) ( 108)  =  54

 

The area can also be expressed as

 

54   =  (1/2) base * z

 

54  = (1/2) 15 * z

 

108 = 15 * z

 

z = 108/15 =  36/5

 

So

 

x + y + z  =    15  + 36/5 =     [ 75 + 36 ]  /  5  =   111  / 5

 

 

cool cool cool

 Dec 29, 2020
 #3
avatar+11 
+5

Because this triangle is a right triangle, by the Pythagorean theorem, we can figure out the hypotenuse by square rooting the sum of the square of the two legs, 9^2+12^2=sqrt225. The sqrt of 225 is 15 so x+y=15. Now we figure out the area of the big triangle. 9*12/2=54. Another way of calculating the area is by multiplying 15 by z and dividing by 2. Since we already figured out the area of the big triangle is 54, we can substitute 54 as the area and we get 54=z*15/2. Solving for z we get 7.2. x+y+z=15+7.2=22.2

 Dec 29, 2020
edited by mimi997  Dec 29, 2020
 #4
avatar+114171 
+2

THX, mimi997   !!!

 

cool cool cool

CPhill  Dec 29, 2020

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