Question

Part A:

Question:

Tonya has a rectangular rug with an area of 54 square feet. The rug is 3 feet longer than it is wide. Create an equation that can be used to determine the length and width of the rug. Justify your answer.

A)
Length
=
Width
+
3
Length=Width+3, Equation:
Length
×
Width
=
54
Length×Width=54

B)
Length
=
Width
−
3
Length=Width−3, Equation:
Length
×
Width
=
54
Length×Width=54

C)
Length
=
3
Width
Length=3Width, Equation:
Length
×
Width
=
54
Length×Width=54

D)
Length
=
54
Width
Length=
Width
54
​
, Equation:
Length
=
Width
+
3
Length=Width+3

Part B:

Question:

Tonya adds a 1.5-foot border all the way around the rug. What is the area of the enlarged rug? Show ALL work.

A)
Area of enlarged rug
=
(
Length
+
3
)
(
Width
+
3
)
Area of enlarged rug=(Length+3)(Width+3)

B)
Area of enlarged rug
=
(
Length
−
3
)
(
Width
−
3
)
Area of enlarged rug=(Length−3)(Width−3)

C)
Area of enlarged rug
=
(
Length
+
1.5
)
(
Width
+
1.5
)
Area of enlarged rug=(Length+1.5)(Width+1.5)

D)
Area of enlarged rug
=
(
Length
−
1.5
)
(
Width
−
1.5
)
Area of enlarged rug=(Length−1.5)(Width−1.5)

Answer 1

The correct equation for the rug's dimensions is Length = Width + 3, and the area is Length × Width = 54. For the enlarged rug after adding a border, the area is given by the equation (Length + 3) × (Width + 3).

Step-by-step explanation:

For Part A, the correct equation to determine the length and width of the rug, given that the rug is 3 feet longer than it is wide and has an area of 54 square feet, is Length × Width = 54 with Length = Width + 3. This corresponds to option A. We justify this by setting up an equation representing the area (length × width) and noting that since the rug is rectangular and 3 feet longer than wide, the length can be expressed as the width plus 3 feet.

For Part B, with Tonya adding a 1.5-foot border around the rug, the area of the enlarged rug is calculated by adding 3 feet to each dimension (since adding 1.5 feet to each side of the rug effectively adds 3 feet to the total length and width). Therefore, the correct equation for the area of the enlarged rug is Area of enlarged rug = (Length + 3) × (Width + 3), which corresponds to option A.