A contractor is installing carpet in a new house. The rectangular living room has an area of 96 square feet, and the length is 12 feet less than three times the width of the room. What are the dimensions of the room?
Answers
Solution :-
Given : The rectangular living room has an area of 96 square feet.
Let the breadth be x.
Length = 3x - 12
According to the question,
=> Area of rectangle = (Length × Breadth) sq. units
=> (3x - 12) × x = 96
=> 3x² - 12x = 96
=> 3x² - 12x - 96 = 0
=> 3x² - 24x + 12x - 96 = 0
=> 3x(x - 8) + 12(x - 8) = 0
=> (3x + 12) (x - 8) = 0
=> x = - 4 or 8
∴ x = 8 (because length is taken positive)
Hence,
Breadth = x = 8 feet
Length = 3x - 12 = 3 × 8 - 12 = 12 feet
Answer :
Length = 12 feet
Width = 8 feet
Step By Step Explanation :
Given :
The rectangular living room has an area of 96 square feet.
Now,
Let assume the required width be k.
Then, Required length = 3k - 12
According To The Condition,
Area of rectangle = Length × Width
⇒ 96 = (3k - 12) × k
⇒ 96 = 3k² - 12k
⇒ 3k² - 12k - 96 = 0
⇒ 3k² - 24k + 12k - 96 = 0
⇒ 3k (k - 8) + 12 (k - 8) = 0
⇒ (3k + 12) (k - 8) = 0
⇒ k = - 4 or 8
∴ k = 8 (Always Take Positive Value)
Therefore,
Width = k = 8 feet
Length = 3k - 12 = 3 × 8 - 12 = 12 feet