Question

what is the length and width of a rectangle with a perimeter of 68cm if width in 2cm less than 8 times the length?

Answer 1

You have to determine the dimensions of a rectangle knowing that its perimeter is 68cm and the width is 2cm less than 8times the length

Let "x" represent the length of the rectangle, then the width can be expressed as "8x-2"

l= x

w= 8x-2

The formula of the perimeter is

`P=2w+2l`

Replace the formula with the expressions determined for the width and length

`68=2(8x-2)+2x`

-Distribute the multiplication on the parentheses term:

`\begin{gathered} 68=2\cdot8x-2\cdot2+2x \\ 68=16x-4+2x \\ 68=16x+2x-4 \\ 68=18x-4 \end{gathered}`

-Pass 4 to the left side of the equal sign by applying the opposite operation to both sides of it

`\begin{gathered} 68+4=18x-4+4 \\ 72=18x \end{gathered}`

-Divide both sides by 18

`\begin{gathered} (72)/(18)=(18x)/(18) \\ 4=x \end{gathered}`

Now you can determine the width of the rectangle:

`\begin{gathered} w=8x-2 \\ w=8\cdot4-2 \\ w=32-2 \\ w=30 \end{gathered}`

The length of the rectangle is l= 4cm and the width is w=30 cm