Question

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.

Answer 1

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