Question

A rectangle has a length 2 m less than twice its width. When 4 m are added to the width, the resulting figure is a square with an area of 100 m^2. Find the dimensions of the original rectangle.

Answer 1

you have a rectangle whose dimensions are w and (2w-2)
add 4 to the width to get w+4
now you have a square whose area is 100 sq m
A=l*w
100=(2w-2)(w+4)
100=2w2-2w+8w-8
100=2w2+6w-8
0=2w2+6w-8-100
0=2w2+6w-108
divide by 2
w2+3w-54=0
factor
(w+9)(w-6)=0
w-6=0
w=6m for the original width

2w-2=2*6-2=12-2=10 m for the original length
if you add 4 to 6 you get 10, and 10*10=100 sq m