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Jessica made plans to weave a rectangular jute rug, but she needs to update the plans to change the dimensions of the rug. The original design has a length of 36 inches and a width of 60 inches. The rug from the new plans will be 3x inches longer and x inches wider than the rug in the original plans. Which of the following functions will give the area of the rug with the new dimensions, in square inches?

User Gaurawerma
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2 Answers

5 votes

Answer:

3x^2+216x+2160

Explanation:

User Laerte
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4 votes

Answer:

Length of rug in original design is 36 inches .

Width of rug in original design is 60 inches .

The problem says that the new design has length 3x inches longer and x inches wider than the rug in the original plans .

New length of rug would be 3x inches longer than the original design which is 36 inches .

Thus new length of rug is ( 3x + 36 ) inches .

New width of rug is x inches wider than the rug in the original plans which is 60 inches in original plan .

Thus new width of rug is ( x + 60 ) inches .

Area of rectangle is Length * Width

Area of new rug is ( 3x + 36 ) * ( x + 60 )

We distribute the terms using FOIL method .

( 3x + 36 ) *( x + 60 ) = 3x ( x + 60 ) + 36 ( x + 60 )

= 3x² + 3x * 60 + 36 x + 36 * 60

= 3x² + 180 x + 36 x + 2160

Combining like terms , 3x² + 216 x + 2160

Thus the area of the rug with the new dimensions is

( 3x + 36) ( x + 60 ) = 3x² + 216 x + 2160 .

User Tajma
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