Tonya has a rectangular rug with an area of 21 ft.² the rug is 4 feet longer than it is wide

Question

A. Create any Quetion that can be used to determine the length and the width of the rug. Justify answer.

B.Tanya adds a 1.5 feet Border all the way around the rug. What is the area of the in large the rug? Show all your work.

Answer 1

Area = length x width = (w) x (w+4) We are told the the length is 4 ft longer than the width

So (w)(w+4)=21

w^2 +4w-21=0

(w+7)w-3)=21. Two solutions w=-7. W=3. We can discard w=-7 since we cannot have a negative distance as the answer for a side

So width= 3 length=7

If we add a 1.5 ft border both dimensions increase by 1.5 to 4.5 and 8.5

New area (4.5)(8.5)= 38.25