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
