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What is the rectangle's height and base?

 

 Aug 22, 2020
 #1
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+2

x (x + 9) = 112

 Aug 22, 2020
 #2
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height times base equals area  ...      h • b = A 

 

                                                          x • (x + 9) = 112  

 

multiply it out                                     x2  + 9x = 112 

 

subtract 112 from both sides             x2 + 9x – 112 = 0  

 

factor the quadratic                           (x + 16)(x – 7) = 0  

 

set each factor equal to zero             x + 16 = 0   so  x = –16    discard, because a side can't be negative    

                                                                                                  at least not in three-dimensional space  

 

                                                          x – 7 = 0     so  x = 7    this is the height 

 

base equals 9 more than height                          7 + 9 = 16   this is the base 

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 Aug 23, 2020

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