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A right triangle with a perimeter of 60 units has an altitude (to the hypotenuse) of length 12 units. Find the sum of the lengths of the two (non-hypotenuse) legs of this triangle.

 Jan 17, 2021
 #1
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Call   a, b  the legs  and the  hypotenuse, c

 

a + b +  c   = 60

 

a +  b =   60 - c                square both sides

 

a^2  + 2ab + b^2   =   3600 - 120c + c^2

 

Note   a^2 + b^2  = c^2

 

So....we have that

 

2ab  = 3600  - 120c

 

ab  =  1800 - 60c     (1)

 

Area of  triangle   = (1/2)  ab

Also

Area =   (1/2)c *12       so

 

(1/2)ab = (1/2) 12c

 

ab  =  12c        (2)        sub  (1)  into (2)

 

1800  - 60 c  =  12c

 

1800  =  72c

 

c = 25

 

a + b =   60  - c

 

a + b  =  60 -  25

 

a + b  =  35  =   sum of the leg lengths

 

cool cool cool

 Jan 17, 2021
 #2
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Good job!!!

 

a = 15        b = 20

Guest Jan 17, 2021

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