### All PSAT Math Resources

## Example Questions

### Example Question #321 : Plane Geometry

A rectangle has a width of 2*x*. If the length is five more than 150% of the width, what is the perimeter of the rectangle?

**Possible Answers:**

6*x*^{2} + 10*x*

6*x*^{2} + 5

10(*x* + 1)

5*x* + 10

5*x* + 5

**Correct answer:**

10(*x* + 1)

Given that *w* = 2*x* and *l* = 1.5*w* + 5, a substitution will show that *l* = 1.5(2*x*) + 5 = 3*x* + 5.

*P* = 2*w* + 2*l* = 2(2*x*) + 2(3*x* + 5) = 4*x* + 6*x* + 10 = 10*x* + 10 = 10(*x* + 1)

### Example Question #1 : How To Find The Perimeter Of A Rectangle

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?

**Possible Answers:**

**Correct answer:**

The length of the garden, in feet, is feet less than that of the entire lot, or

;

The width of the garden, in feet, is less than that of the entire lot, or

.

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

### Example Question #12 : Rectangles

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*?

**Possible Answers:**

**Correct answer:**

The inner square, which represents the garden, has sidelength feet, so its perimeter is four times this:

feet.

### Example Question #31 : Quadrilaterals

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?

**Possible Answers:**

180 yards

170 yards

200 yards

160 yards

210 yards

**Correct answer:**

180 yards

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.

### Example Question #1 : How To Find The Perimeter Of A Rectangle

A rectangular garden has an area of . Its length is meters longer than its width. How much fencing is needed to enclose the garden?

**Possible Answers:**

**Correct answer:**

We define the variables as and .

We substitute these values into the equation for the area of a rectangle and get .

or

Lengths cannot be negative, so the only correct answer is . If , then .

Therefore, .

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