9.4 #13 word problem

Question

A rectangle has a length 2m less than twice its width. When 5m are added to the width, the resulting figure is a square with an areas of 144m squared. find the dimensions of the original rectangle.

 

The original rectangle has a width of ___m and a length of ___m.

Answer 1

you have a rectangle whose dimensions are w and (2w-2)

add 5 to the width to get w+5

now you have a square whose area is 144 sq m

A=l*w

144=(2w-2)(w+5)

144=2w²-2w+10w-10

144=2w²+8w-10

0=2w²+8w-10-144

0=2w²+8w-154

divide by 2

w²+4w-77=0

factor

(w+11)(w-7)=0

w-7=0

w=7 m for the original width

2w-2=2*7-2=14-2=12 m for the original length

if you add 5 to 7 you get 12, and 12*12=144 sq m