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The perimeter of the entire figure is 86 cm, and the sum of the areas of the two squares is 386 cm^2. In centimeters, what is the value of a + b ?

 May 22, 2020
 #1
avatar+111321 
+2

We  have  that

 

3a  + (a - b)  +  3b   =  86 

 

4a + 2b  =  86       divide through by 2

 

2a  + b =  43

 

b  =  43 - 2a       (1)

 

     and

 

a^2  + b^2  =  386      (2)        sub (1) into (2) for b

 

a^2  + (43 - 2a)^2  =  386     simplify

 

a^2  + 4a^2  - 172a  + 1849  =  386         subtract   386  from both sides

 

5a^2  - 172a  + 1463   =   0      this will factor as

 

(5a  - 77)  (a - 19)  = 0

 

The second factor set to 0 and solved for "a"  gives us an integer solution....

 

a =19

And  b =  43 - 2(19)  =  5

 

So.....a + b  =   24

 

 

cool cool cool

 
 May 22, 2020

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