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A right triangle has legs of length  6 and b, and a hypotenuse of length c . The perimeter of the triangle is 18 . Compute c.

mathtoo  Aug 13, 2018
 #1
avatar+147 
+3

Hint: Difference of Squares!
a^2+b^2=c^2, c^2-b^2=a^2, (c+b)(c-b)=36.

You also know the perimeter is 18, so 6+b+c=18, b+c=12.

So, (12)(c-b)=36, c-b=3..

Now, we have two equations, and if we subtract, we will get: c=7.5

azsun  Aug 13, 2018
 #2
avatar+91186 
+2

Thanks, azsun...here's one more way.....

 

We have that   6 + b + c  = 18   ⇒   c = [18 - 6  - b]  =  [12  - b]

 

So...using the  Pythagorean Theorem

 

6^2  + b^2  = (12 - b)^2

36 + b^2  = 144 - 24b + b^2

24b - 108  = 0

24b  = 108

2b  = 9

b  = 9/2  = 4.5

 

So...c  =  12  - 4.5  =  7.5

 

 

cool cool cool

CPhill  Aug 13, 2018
 #3
avatar+621 
+1

Thanks! Very good! laugh

mathtoo  Aug 21, 2018

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