Algebra word problem

Question

A rectangle is 3 feet longer than it is wide. If the width is doubled and the length is decreased by 1 foot, the new area is 42 square feet more than the original area. Find the dimensions of the original rectangle.

 

 

 

please show work.

 

 

thans!

Answer 1

Original Rectangle

width = w

length= w+3

 

area =w(w+3)

 

modified rectangle

width =2w

length =(w+3) -1 =w+2

area =2w(w+2)

 

modified rectangle area > original rectangle area

 

2w(w+2) =w(w+3) + 42

 

2w²+4w =w²+3w+42

 

w²+w-42 =0

 

(w+7)(w-6)=0

w=-7, w=6

 

Original Rectangle
width = w =6
length= w+3 =9

 

Answer 2

Setup: Original rectangle is x by x+3

Altered rectangle: 2x  by x+2 (assuming original width was the lesser side length).

 

Now write equation involving area relationship:  2x(x+2) = x(x+3) +42.

 

Solve for x.