Answer: Dimensions of the sheet are 21 x 12
Option D. w^2 + 9w - 252 = 0 , is the equation for the given word
problem.
Step-by-step explanation: Area of rectangle = length x width
Here, Area of rectangle = 252
width = w
length = ( 9+w ) , as per the question
( 9+w) (w) = 252
9w + w^2 = 252
=> w^2 + 9w - 252 = 0 ( option D )
w^2 + 21w - 12w - 252 = 0
w(w + 21 ) - 12 ( w + 21 ) = 0
( w - 12 ) ( w + 21 ) = 0
w = 12 or w = - 21
Width cannot be negative. Therefore only 12 can be considered as the value for width.
w = 12 ( inches )
Since length is 9 inches longer than the width =>
l = ( 9 + w )
= 9 + 12
= 21
therefore, length ( l ) = 21 ( inches )
The dimensions are 21 x 12
Verification :
Area of rectangle = l x w
252 = 21 x 12
252 = 252