Question

the length of a rectangle is 4 ft more than twice the width. the area of a rectangle is 48 ft² . find the width and the length of the rectangle.​

Answer 1

Given :

The length of the rectangle is 4 ft more than twice the width.

Area of the rectangle = 48ft²

To Find: Length and Width of the rectangle

Solution:

Let the width of the rectangle be 'x'

Let the length of the rectangle be 'y'

y = 2x + 4         (Given)             ....(i)

Area of rectangle = Length x Width

48 = (2x+4) (x)

48 = 2x² + 4x                   (on simplifying the brackets)

2x² + 4x - 48 = 0

2(x² + 2x - 24) = 0

x² + 2x - 24 = 0

This quadratic equation can also be written as

x² + 6x - 4x - 24 = 0          

x(x + 6) - 4(x + 6) = 0        [on taking (x + 6) common]

(x - 4) (x + 6) = 0

from the above equation we get

x = 4 or x = -6

As the value of width can't be negative so we reject x = - 6

So, x = 4

We can find the value of y by placing the value of x in eq. (i)

y = 2x + 4

y = 2(4) + 4

y = 8 + 4

y = 12

Therefore, the width of the rectangle is 4ft and the length is 12ft.