"the perimeter of a rectangle is 42 centimeters. the length of the rectangle can be represented by (x+4), and the width can be represented by (2x-7). what are the dimensions of this rectangle in centimeters"

Perimeter is the sum of all the sides. One length equals (x+4) so both of the lengths will equal 2(x+4) = 2x+8. One width is (2x-7) so both will equal 2(2x-7) = 4x-14.

we can write this into an equation like so:
2x+8+4x-14=42
6x-6=42
6x=48
x=8

Then we substitute 8 back into the equations for the lengths of the sides.
8+4= 12 so the length is 12cm
2x8= 16, 16-7=9 so the width is 9cm

Answer Link

akposevictor akposevictor · Answer 2 · 2021-10-08T12:21:28+02:00

The dimensions of the rectangle that has a perimeter of 42 cm are:

length = 12 cm

width = 9 cm

Recall:

The perimeter of a rectangle is given as:

Perimeter = 2(length + width)

Given the following:

Length of rectangle = [tex](x+4)[/tex]

Width of rectangle = [tex](2x-7)[/tex]

Perimeter of rectangle = 42 cm

Therefore:

[tex]2((x + 4) + (2x -7)) = 42[/tex]

Open the bracket

[tex]2(x + 4 + 2x -7) = 42[/tex]

Add like terms

[tex]2(3x -3) = 42\\\\6x - 6 = 42\\\\[/tex]

Add 6 to both sides

[tex]6x - 6 + 6 = 42 + 6\\\\6x = 48\\[/tex]

Divide both sides by 6

[tex]x = 8[/tex]

Find the dimensions of the rectangle by plugging in the value of x

[tex]length = (x+4) = 8 + 4 = 12 $ cm\\\\width = (2x - 7) = 2(8) - 7 = 9 $ cm[/tex]

Therefore, the dimensions of the rectangle that has a perimeter of 42 cm are:

length = 12 cm

width = 9 cm

Learn more here:

https://brainly.com/question/18869010