Question

The perimeter of a rectangle is 56 cm . The length of the rectangle can be represented by 6x-7 and it’s width by 2x+3.what are the dimensions of this rectangle in centimeters​

Answer 1

The dimensions of the rectangle are: Length: 17 centimeters, Width: 11 centimeters.

Explanation:

From Geometry we remember that the perimeter (
`p`), measured in centimeters, of a rectangle is determined by the following formula:

`p = 2\cdot w +2\cdot l` (1)

Where:

`w` - Width of the rectangle, measured in centimeters.

`l` - Length of the rectangle, measured in centimeters.

If we know that
`p = 56\,cm`,
`l = 6\cdot x - 7` and
`w = 2\cdot x + 3`, then the value of
`x` is:

`2\cdot (2\cdot x +3)+2\cdot (6\cdot x-7) = 56`

`4\cdot x +6 +12\cdot x -14 = 56`

`16\cdot x-8 = 56`

`16\cdot x = 64`

`x = 4`

And the length and the width of the rectangle are, respectively:

`l = 6\cdot (4)-7`

`l = 17\,cm`

`w =2\cdot (4)+3`

`w = 11\,cm`

The dimensions of the rectangle are: Length: 17 centimeters, Width: 11 centimeters.