The area of a rectangular library room is 60 squared meter. Find the perimeter of the room given that its length is 3 meter more than thrice its width.
Representation:
Let width = x meter
length = 3x + 3 meter
Area = 60 m²
Area of Rectangle = Length × Width
60 = (3x+3) (x)
60 = 3x² + 3x
Equate to zero (this a quadratic equation)
3x² + 3x - 60 = 0
Solve by factoring:
3 (x² + x + 20) = 0
3 (x-4) (x+5) = 0
x-4 = 0 x + 5 = 0
x = 4 x = -5
Choose the positive value x = 4
Width: x = 4 meters
Length: 3x + 3
= 3(4) + 3
= 12 + 3
= 15 meters
Perimeter of a rectangle: 2 (L) + 2 (W)
P = 2 (15 meters) + 2 ( 4 meters)
P = 30 meters + 8 meters
P = 38 meters
The perimeter of the rectangular library room is 38 meters.
