Answer:
The dimensions of the rectangle are: Length: 17 centimeters, Width: 11 centimeters.
Step-by-step explanation:
From Geometry we remember that the perimeter ([tex]p[/tex]), measured in centimeters, of a rectangle is determined by the following formula:
[tex]p = 2\cdot w +2\cdot l[/tex] (1)
Where:
[tex]w[/tex] - Width of the rectangle, measured in centimeters.
[tex]l[/tex] - Length of the rectangle, measured in centimeters.
If we know that [tex]p = 56\,cm[/tex], [tex]l = 6\cdot x - 7[/tex] and [tex]w = 2\cdot x + 3[/tex], then the value of [tex]x[/tex] is:
[tex]2\cdot (2\cdot x +3)+2\cdot (6\cdot x-7) = 56[/tex]
[tex]4\cdot x +6 +12\cdot x -14 = 56[/tex]
[tex]16\cdot x-8 = 56[/tex]
[tex]16\cdot x = 64[/tex]
[tex]x = 4[/tex]
And the length and the width of the rectangle are, respectively:
[tex]l = 6\cdot (4)-7[/tex]
[tex]l = 17\,cm[/tex]
[tex]w =2\cdot (4)+3[/tex]
[tex]w = 11\,cm[/tex]
The dimensions of the rectangle are: Length: 17 centimeters, Width: 11 centimeters.
