Question

A clothing store has a rectangular clearance section with a length that is twice the width w. During a sale, the section is expanded to an area of (2w^2 + 11w + 12) ft^2. Find the amount of the increase in the length and width of the clearance section.

Answer 1

Answer:

see the explanation

Step-by-step explanation:

step 1

The original area of the rectangular clearance section is equal to

$A=LW$ ----> equation A

we know that

The length is twice the width

$L=2W$ ----> equation B

substitute equation B in equation A

$A=(2W)W$

$A=2W^2\ ft^2$

step 2

During a sale, the section is expanded to an area of

$A=(2W^2+11W+12)\ ft^2$

so

To find out the amount of the increase in the length and width of the clearance section, subtract the areas

$(2W^2+11W+12)\ ft^2-2W^2\ ft^2=(11W+12)\ ft^2$

therefore

The amount of the increased area is $(11W+12)\ ft^2$