+0  
 
0
111
3
avatar

A right triangle has legs of length  6 and b, and a hypotenuse of length c . The perimeter of the triangle is 24 . Compute c.

 Dec 14, 2020
 #1
avatar
+1

C is 10

 

With pythag, we have 6^2 + b^2 = c^2

36 + b^2 = c^2

c = \sqrt{36+b^2}

so now we have 6+b+\sqrt{36+b^2} = 24

After some ugly math, b=8

 

6^2 + 8^2 = c^2

100 = c^2

c = 10

 

check: 6^2 + 8^2 = 10^2

100 = 100

 

:)

 Dec 14, 2020
 #2
avatar
+1

Oh and perimeter check

 

10+8+6 = 14+10=24

Guest Dec 14, 2020
 #3
avatar+117546 
+1

6 + b + c  = 24

b + c =  18

b = 18 - c

 

So....by the Pyth. theorem

 

6^2  + (18 - c)^2   = c^2

 

36  + c^2  - 36c + 324  = c^2

 

360 - 36c   =   0       divide  through by 36

 

10  - c    = 0

 

c  = 10

 

cool cool cool

 Dec 14, 2020

68 Online Users

avatar
avatar
avatar
avatar