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A sheet of metal is 9 inches longer than it is wide, and its total area is 252 square inches. Find the dimensions of the sheet of metal.

If w represents the width of the metal sheet, which of the following equations is a model for the given word problem?
A. w^2-9w-252=0
B. w^2-9w+252=0
C. w^2+9w+252=0
D. w^2+9w-252=0

User Chobeat
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1 Answer

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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

User Martin Ernst
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