Algebra question

Question

the length of a particular rectangle is 10 feet more than 4 times its width Find the length and width if the area of the rectangle is 113 square feet

Answer 1

Let w = the width of the rectangle

Let 4w + 10 = the length of the rectangle

A = lw

113 = w(4w + 10)

113 = 4w² + 10w

4w² + 10w - 113 = 0

                                                                            

w = -b ± √b² -4ac   = -10 ± √10² - 4(4)(-113)

               2a                               2(4)

                                                                

w = -10 ± √100 +1808 =  -10 ± √1908

                    8                              8

 

w = -10 ±43.68

               8

 

w = -10 + 43.68         w = -10 - 43.68

              8                                  8

 

w = 4.21 feet            w = -6.71 (illogical answer

l = 4w + 10

l = 26.84 feet