word problem

Question

a square field had 5m added to its length and 2m added to its width. the area of the field was then 130m^2. find the length of a side of the original field.

Answer 1

 

 

We call by L the original length  and W the original width. But, the original field was a square, then W=L.

 

Now, we increased L by 5m (= L+5) and W by 2m (= W+2 = L+2).

 

As a result, the new field has a rectangular shape (L is not longer equal to W, as the original square field was).

 

The area of this rectangular field is:   (L+5)(L+2) = 130

                                                     

                                                         L² + 7L + 10 = 130

 

                                                         L² + 7L - 120 = 0

 

Solving this quadratic equation by the appropriated method, we have two values of L:

 

L = (-7 + 23)/2 =  8 m       and 

 

L = (-7 - 23)/2  = -15 m  (this is not physically possible, and is discharged)

 

 

Then, the original square field has a length L = 8 m  and width = 8 m

 

Proof:  Rectangular field length =  L + 5  = 13 m    

 

          Rectangular field width =  L + 2 = 10 

 

          Area = L*W = (13)*(10) = 130 m2

                                                       

 

 

Answer 2

(x + 5)(x + 2) = 130          area of square

x² + 7x + 10 = 130            FOIL

x² + 7x - 120 = 0               subtract 130 from both sides

(x + 15)(x - 8) = 0            FOIL

 

zero product rule

 

x = 8 (measure cannot be negative)