the length of a rectangle is 1 less than 2 width. the area of the rectangle i 45 cm2. find the length and the width

Question

solving word problem with quadratic equations

Answer 1

Let the W=width of rectangle                 Then one less than twice the width              length =L=2W-1           

 

A=Area of rect.   A=45 sq. cm

 

The formula for the area of a rectangle is the following:   A=L*W.

 

 

Now substitute what was given into the equation:      45= (2W-1)*W  

 

                                                                           45=   (2W²  -W)      

                                                                           

                                                                           0=  2W²  -W-45             Take away 45 from both sides.  

                  

                                                    Finally, I suggest you use the Quadratic Formula to find width. 

 

     Remember the Standard form for a parabola:     y=aX²  + bX+  C.

 

 

List the values of coefficients (numbers next to  letters).      0=2W² -1 W  -45                         

 

                                                So a= 2           b=-1          and C=-45

 

 

Use this formula:         W=  (-b +or -  √(b² -4ac))         ^{Divide everything on right by 2a.} 

                                                                  ^2a      

 

 

                                width=W=  (  -(-1)  +/-  √((-1)²-4(2)(-45))

                                                               2(2)

 

You will get two answers for W.  One is a positive and one is negative.  Since length is not negative, use the positive answer.  After you get "w," just substitute  to find the length, L=2W-1.