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Given a triangle ABC in which $ AB = x+3 $ and $ BC = x-1 $ and $\angle ABC = 30° $, its area is $ 35 \text{cm}^{2} $. Find $ AB+BC $.

 Feb 5, 2021
 #1
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Area = (1/2)  ( AB) ( BC)   sin 30

 

35 =   (1/2)  ( x + 3) ( x -1)  (1/2

 

35  =  (1/4)( x + 3)  ( x -1)    multiply through  by 4

 

140  =  (x + 3) ( x -1)

 

140   = x^2   +   2x  - 3        rearrange as

 

x^2 + 2x    -143  =  0        factor as

 

(x - 11)  ( x + 13)   =  0

 

The first factor  set to  0   gives us what we need

 

x - 11   =   0

 

x  =11

 

AB  = x + 3   =14

BC  = x  - 1   = 10

 

AB  + BC    = 24

 

 

cool cool cool

 Feb 5, 2021

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