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Worksheet: Applications of Perimeters of Squares and Rectangles

Q1:

A rectangular field with dimensions 68 m and 43 m is surrounded by a fence. The field contains a square playground with side length 13 m that also has a fence around it. Calculate the total length of fence around the field and the playground.

Q2:

A rectangular field with dimensions 68 m and 49 m is surrounded by a fence. The field contains a square playground with side length 17 m that also has a fence around it. Calculate the total length of fence around the field and the playground.

Q3:

The perimeter of a rectangle is 16 cm. If the length is 𝑥 cm, write an expression for the width.

  • A ( 𝑥 1 6 ) cm
  • B ( 8 + 𝑥 ) cm
  • C ( 1 6 𝑥 ) cm
  • D ( 8 𝑥 ) cm

Q4:

The Parkers are building a fence around their rectangular yard that is 52 feet long and 29 feet wide. How much fence will they need?

Q5:

The given diagram shows the floor plan of the David’s house. Which of the rectangular rooms has the greatest perimeter?

  • AJennifer’s bedroom
  • BMatthew’s bedroom
  • Cthe living room
  • DDavid’s bedroom
  • Ethe kitchen

Q6:

A frame needs to be designed for a rectangular picture whose dimensions are 35 cm and 15 cm. Given that the frame costs 3 LE per metre, find the cost of the frame.

Q7:

Benjamin’s back yard measures 46 by 29 feet, while his front yard is a square with a side length of 38 feet. If Benjamin decides to fence both of them, determine the length of the fencing he will need to do so.

Q8:

Liam’s back yard measures 42 by 30 feet, while his front yard is a square with a side length of 40 feet. If Liam decides to fence both of them, determine the length of the fencing he will need to do so.

Q9:

A man has a square-shaped garden with length 16 metres that he wants to surround with a fence. If one metre of the fence costs 7 LE, how much will the fence cost?

  • A112 LE
  • B64 LE
  • C224 LE
  • D448 LE

Q10:

A fence around a rectangular garden has a length of 164 feet and a width of 109 feet. Determine the length of the fence.

Q11:

If a keyboard’s rectangle-shaped has dimensions of 45 cm and 150 mm, what is its perimeter in centimeters?

  • A 390 000 cm
  • B 390 cm
  • C 195 cm
  • D 120 cm
  • E 6 750 cm

Q12:

A square ballet studio has an area of 1 369 square feet. A carpenter has been asked to install a barre around the perimeter of the studio. What is the total length of the barre?

Q13:

The width of a rectangle is 𝑥 cm and its length is twice its width. Write an expression for its perimeter in cm.

  • A ( 4 + 2 𝑥 ) cm
  • B ( 6 + 2 𝑥 ) cm
  • C 4 𝑥 cm
  • D 6 𝑥 cm

Q14:

Calculate, in decimeters, the length of a rectangle whose perimeter is 190 cm and width is 35 cm.

  • A 11 dm
  • B 60 dm
  • C 15 dm
  • D 6 dm
  • E 5 dm

Q15:

The perimeter of a square is 108 cm. A smaller square has side lengths that are 9 cm shorter than the sides of the first square. Find the perimeter of the smaller square.

Q16:

Determine the perimeter of the shape below.

Q17:

Ethan wants to add fringes to all the sides of a rectangular rug for her bedroom. Given that the rug is 4.5 feet wide and 5 feet long, determine how many feet of fringe she needs.

Q18:

A rectangular park has dimensions of 150 by 93 feet. There is a 3-foot-wide sidewalk that borders each side of this park. What is the outer perimeter of the sidewalk that encloses the neighborhood park?

Q19:

A square carpet has a side length of 10 m, and a rectangular carpet has a length of 13 m. Given that the two carpets have the same perimeter, find the width of the rectangular carpet.

Q20:

A square carpet has a side length of 5 m, and a rectangular carpet has a length of 7 m. Given that the two carpets have the same perimeter, find the width of the rectangular carpet.

Q21:

How many rectangles can be drawn in the given grid, such that the vertices of each rectangle coincide with four of the dots and that each rectangle’s perimeter equals 8 cm?

Q22:

Determine the perimeter of a poster that is 47 inches long and 30 inches wide.

Q23:

Hannah is building a fence around her rectangular garden. The garden is 43 feet wide and 56 feet long. Fences can only be bought in sections that are 18 feet long, but they can be cut to size after purchase. How many sections does she need to buy?

Q24:

Lucy has a 216-feet-long fence around her garden. If her garden is in the shape of a square, determine the length of each side.

Q25:

Holly has a 64-feet-long fence around her garden. If her garden is in the shape of a square, determine the length of each side.