Question

HELP ME PLEASE!!! Question 1Jim is planning his spring garden. He will construct a rectangular gardensurrounded by a chain link fence. The length of Jim's garden will be 8 feet morethan 3 times its width (w).(Drawing and labeling a diagram may be helpful)Part A: Write an expression in terms of w to represent the amount of chain linkfencing (the perimeter) Teeded to enclose Jim's garden.

Answer 1

We have a rectangular garden.

The length L is 8 feet more than 3 times its width.

3 times the width is 3w, so we will add 8 to it and equal it to the length L:

`L=8+3w`

The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:

`\begin{gathered} P=2L+2w \\ P=2(8+3w)+2w \\ P=16+6w+2w \\ P=16+8w \end{gathered}`

The perimeter has a value of P=16+8w.

We can draw the diagram as:

Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?

We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.

`\begin{gathered} P=16+8w \\ 88=16+8w \\ 88-16=8w \\ 72=8w \\ w=(72)/(8) \\ w=9.75 \end{gathered}`

The width is 9.75 feet.