Question

Sammie bought just enough fencing to border either a rectangular plot or a square plot,

shown. The perimeters of the plots are the same. How many feet of fencing did she buy?


(3x + 6) feet.

———————

| |

| | (x - 1) feet

|__________|


(x + 6) feet

___________

| |

| |

| | (x + 6) feet

| |

|__________ |


Sammie bought____feet of fencing.

Answer 1

3.5 feet

Explanation:

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We have:

(x + 6) feet on each side of the square

(3x + 6) feet horizontally on the rectangle

(x - 1) feet vertically on the rectangular

First, we need to determine the perimeter of the square:

`Perimeter = 4 * Length`

`Perimeter = 4 * (x + 6)`

`Perimeter = 4x + 24`

Next, we determine the perimeter of the rectangle

`Perimeter = 2(Length + Width)`

`Perimeter = 2(3x + 6 + x - 1)`

`Perimeter = 2(3x + x+ 6 - 1)`

`Perimeter = 2(4x+ 5)`

`Perimeter = 8x+ 10`

Equate both perimeters:

`8x + 10 = 4x + 24`

Collect Like Terms

`8x - 4x = 24 - 10`

`4x = 14`

Solve for x

`x = 14/4`

`x = 3.5`