The length of the rectangle = 16 meters
The width of the rectangle = 10.5 meters
Step-by-step explanation:
Given that,
The Area of the rectangle is 273.
Step 1 :
Let, the width of the rectangle be 'x'
The length of the rectangle is 2x - 5
Step 2 :
Area of the rectangle = length [tex]\times[/tex] width
273 = (2x - 5) x
273 = 2x^2 - 5x
Step 3 :
The equation formed is 2x^2 - 5x -273 = 0
a= coefficient of x^2 = 2
b= coefficient of x = -5
c = constant = -273
Find the roots of the equation, to find the width.
Step 4 :
Find the roots using factorizing method,
ac = 2[tex]\times[/tex]-273 = -546 and b= -5
Factorizing -546 as -26[tex]\times[/tex]21
The product of -26[tex]\times[/tex]21 = -546
The sum of -26 + 21 = -5
Step 5 :
The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2
The values of x are x= -13 and x= 10.5
Since the width cannot be a negative value, neglect x= -13
Step 6 :
Therefore,
The width of the rectangle = 10.5 meters
The length of the rectangle = 2x-5
= 2(10.5) - 5
= 21 - 5
length = 16 meters