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

Question

asked May 7, 2021 104k views

1 Answer

Shakisha · Answer 1 · 2021-05-13T05:07:11+0000

Answer:

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

Explanation:

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

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

Where:

- Width of the rectangle, measured in centimeters.

- 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
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.