Question

Unit 5 Solving Systems of EquationsNameDay 4 Notesthe width. Find the length and width of the garden.4. The perimeter of a rectangular garden is 36 feet. The length of the garden is 6 less than twiceVariable:Equation:Variable:Equation:LengthWidth

Answer 1

The perimeter of the rectangular garden is 36 feet

The length of the garden is 6 feet less than twice the width.

Let x represent the width of the garden:

w=x

Then we can multiply it by 2 and subtract 6 to determine the length:

l=2x-6

Lets sketch the garden:

The perimeter of a rectangle is the summ of all its sides, that is twice the width plus twice the length:

`P=2w+2l`

Replace the formula with the given value of P and the expressions for w and l:

`36=2x+2(2x-6)`

And solve for x, first is to apply the distributive propperty of multiplications to solve the term in parentheses:

`\begin{gathered} 36=2x+4x-12 \\ 36=6x-12 \\ 36+12=6x \\ 48=6x \\ (48)/(6)=(6x)/(6) \\ 8=x \end{gathered}`

The width of the garden is 8 feet

Now calculate the length of the garden:

`\begin{gathered} l=2x-6 \\ l=2\cdot8-6 \\ l=16-6 \\ l=10 \end{gathered}`

The length of the garden is 10 feet