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

Answer:

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

Step-by-step 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.