Tonya has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it is wide. Create an equation that can be used to determine the length and the width of the rug. Tonya adds a 1.5-foot boarder all the way around the rug. What is the area of the enlarged rug? Show all work.

a) The equations to determine the length and the width of the rug are

l = 4 + w and l * w = 21

b) The enlarged rug's area = 60 square feet

Step-by-step explanation:

Step 1:

Let l be the length and w represent the width of the rectangular rug

Given the area = 21 square feet.

So l * w = 21

Also given, the length is 4 feet longer than the width.

So we have

l = 4 + w

Step 2:

Using the above 2 equations we have

(4+w) w = 21

w² + 4 w - 21 = 0

(w+7) (w-3) = 0

=> w = - 7 or w = 3

Since w is the width of the rug, we take the positive value w = 3 as the width

So w = 3 feet

So

l = 4 + w = 4 + 3 = 7 feet

Step 3:

When a 1.5 foot border is added all the way round the rug, the length and width are increased by 3 feet (1.5 feet on both sides) the rug's enlarged length and the rug's enlarged width is

l = 7 + 3 = 10

w = 3 + 3 = 6

The enlarged rug's area = 10 * 6 = 60 square feet

Step 4:

Answer:

The equations to determine the length and the width of the rug are

l = 4 + w and l * w = 21

The enlarged rug's area = 60 square feet