ACT Prep Perimeter & Line Segments

The Summerdale Community Council is planning the renovation of a park in the center of the town. The park will be a rectangular region of 85 feet by 175 feet with an area of 14,875 square feet. There will be a wooden fence along the perimeter of the park. What is the total length of the fence, in feet?

• 250

• 340

• 410

• 480

• 520

The length of a rectangle is 8 inches longer than its width. If the perimeter of the rectangle is 36 inches, what is the width, in inches?

• 13

• 10

• 5

• 4

• 3

The figure is composed of equilateral triangle ABD and another equilateral triangle BCD. The length of line AD is 12 inches. What is the perimeter of figure ABCD?

• 12

• 24

• 44

• 48

• 60

A certain square has the same perimeter as a regular pentagon (a 5-sided polygon with all sides and interior angles congruent). If 1 side of the pentagon is 72 millimeters, how long is 1 side of this square?

• 45

• 60

• 75

• 90

• 135

This polygon, whose side lengths are given in meters, has 2 unknown sides. Each angle between adjacent sides measure 90 degrees. What is the polygon's perimeter, in meters?

• 44

• 62

• 80

• 158

• 234

Joseph is constructing a rectangular fence for his garden. A diagram of the fence is shown. Which of the following expressions gives the perimeter of Joseph's fence?

• 3x + 5

• 3x + 10

• 6x + 10

• 6x + 20

• 2x squared + 11x - 6

Justin is centering a mosaic on his bedroom wall. As shown in the figure, the rectangular wall is 28 feet in length, and the mosaic is 3 feet in height and 6 feet in length. The right edge of the mosaic will be y feet from the right edge of the wall, and the left edge of the mosaic will also be y feet from the left edge of the wall. What is the value of y, in feet?

• 9

• 10

• 10.5

• 11

• 12.5

For the line segment, the ratio of the length of XY to the length of YZ is 1:6. If it can be determined, what is the ratio of the length of XY to the length of XZ?

• 1:5

• 1:7

• 3:1

• 7:1

• Cannot be determined from the given information

Points X and Y lie on line WZ. The length of WZ is 36 inches; WY is 16 inches long; and XZ is 28 inches long. How many inches long, if it can be determined, is XY?

• 4

• 8

• 12

• 16

• Cannot be determined from the given information

The perimeter of a parallelogram is 76 inches, and the measure of 1 side is 17 inches. What are the lengths of the 3 remaining sides?

• 17, 17, 17

• 17, 17, 42

• 17, 20, 20

• 17, 21, 21

• Cannot be determined from the given information