PSAT Math - How to find the perimeter of a rectangle

Garden

Note: Figure NOT drawn to scale

Refer to the above figure, which shows a square garden (in green) surrounded by a dirt path (in orange) eight feet wide throughout. What is the perimeter of the garden?

$236 \textup{ ft}$

$268 \textup{ ft}$

$284\textup{ ft}$

$118 \textup{ ft}$

$134 \textup{ ft}$

Explanation

The inner square, which represents the garden, has sidelength $(75 - 2\times 8) = 59$ feet, so its perimeter is four times this:

$P = 4 \times 59 = 236$ feet.

Garden

Note: Figure NOT drawn to scale

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in orange). The dirt path is seven feet wide throughout. Which of the following polynomials gives the perimeter of the garden in feet?

$2x^{2}-42x +196$

$2x^{2}-21x + 49$

Explanation

The length of the garden, in feet, is $2 \times 7 = 14$ feet less than that of the entire lot, or

;

The width of the garden, in feet, is $2 \times 7 = 14$ less than that of the entire lot, or

The perimeter, in feet, is twice the sum of the two:

Farmer Dave has a rectangular field that is 50 yards wide and 40 yards long. He wants to enclose the field with a wire fence. How much wire does Farmer Dave need?

180 yards

200 yards

160 yards

170 yards

210 yards

Explanation

To solve this problem, find the perimeter of the rectangle. There are two sides that each measure 50 yards and two sides that each measure 40 yards. Together these four sides measure 180 yards.

A rectangular garden has an area of $80: \mbox{m^2}$ . Its length is meters longer than its width. How much fencing is needed to enclose the garden?