Question

The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 273 meters, find the dimensions

Answer 1

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 $\times$ 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$\times$-273 = -546 and b= -5

Factorizing -546 as -26$\times$21

The product of -26$\times$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