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The perimeter of a right angle triangle is 112 mm.

The length of the altitude that is perpendicular to the hypotenuse is 13.44 mm.

What is the length, in mm, of the hypotenuse?

 

 Jan 18, 2021
 #1
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a + b + c  =  112         where  a,b are the legs and c is the hypotenuse

a + b     = 112  - c       square both sides

a^2 + 2ab + b^2  =   c^2 - 224c + 12544

Note that  a^2 + b^2  = c^2        so the above becomes

2ab  =  12544  - 224c        (1)

 

The area  of the  triangle is   (1/2) ac

Also   the area   is  (1/2)13.44 * c 

 

So

 

(1/2)ab  =  (1/2) 13.44c     

ab  =  13.44c

2ab  = 26.88c       (2)

 

Sub (2)  into (1)

 

26.88c =  12544 - 224c    add 224c  to both sides

 

26.88 c + 224c =   12544

 

250.88 c   = 12544      divide both sides by  250.88

 

c =  50  = the hypotenuse  length

 

 

cool cool cool

 Jan 18, 2021

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