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Calculate the perimeter of the given shapes and solve a word problem about distance walked.

Mathematics

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2 parts
3

32 cm\text{32 cm}

21 cm\text{21 cm}

4

20 km\text{20 km}

38 m\text{38 m}

Step-by-step solution

12 steps

Here are the solutions for the questions:

Part 3· 6 steps

Calculate Perimeter of given shape

  • Shape 1 (Rectangle):
  1. Identify the length and width of the rectangle.

    Length ($L$) = 9 cm  
    Width ($W$) = 7 cm
    
  2. Use the formula for the perimeter of a rectangle, P=2(L+W)P = 2(L + W).

    $$
    P = 2(9 \text{ cm} + 7 \text{ cm})
    $$
    
  3. Calculate the sum inside the parentheses and then multiply.

    $$
    P = 2(16 \text{ cm})
    $$
    $$
    P = 32 \text{ cm}
    $$
    The perimeter of the first shape is $\boxed{\text{32 cm}}$.
    
    • Shape 2 (Combined shape):
  4. Identify all the outer side lengths of the combined shape.

    The outer sides are 4 cm (top), 3 cm (left), 4 cm (bottom), 5 cm (right slanted), and 5 cm (top slanted).
    
  5. Add all the outer side lengths to find the perimeter.

    $$
    P = 4 \text{ cm} + 3 \text{ cm} + 4 \text{ cm} + 5 \text{ cm} + 5 \text{ cm}
    $$
    
  6. Calculate the sum.

    $$
    P = 21 \text{ cm}
    $$
    The perimeter of the second shape is $\boxed{\text{21 cm}}$.
    

Part 4

20 km\text{20 km}

Word Problem on Length and Perimeter

  • a) Joy lives 2 km away from Panatina Campus. If he walks to Panatina Campus and return home each day. What would be the total distance he walks in 5 days?
  1. Calculate the distance Joy walks in one day (to campus and back home).

    Distance to campus = 2 km  
    Distance back home = 2 km  
    Daily distance = $2 \text{ km} + 2 \text{ km} = 4 \text{ km}$
    
  2. Calculate the total distance walked over 5 days.

    Total distance = Daily distance $\times$ Number of days  
    Total distance = $4 \text{ km/day} \times 5 \text{ days}$
    
  3. Perform the multiplication.

    Total distance = $20 \text{ km}$  
    Joy walks a total distance of $\boxed{\text{20 km}}$.
    
    • b) Joy wants to make fence of timber around her garden. The garden is a rectangular shape. The length is 12 m and the width is 7 m. What is the perimeter of the garden?
  4. Identify the length and width of the rectangular garden.

    Length ($L$) = 12 m  
    Width ($W$) = 7 m
    
  5. Use the formula for the perimeter of a rectangle, P=2(L+W)P = 2(L + W).

    $$
    P = 2(12 \text{ m} + 7 \text{ m})
    $$
    
  6. Calculate the sum inside the parentheses and then multiply.

    $$
    P = 2(19 \text{ m})
    $$
    $$
    P = 38 \text{ m}
    $$
    The perimeter of the garden is $\boxed{\text{38 m}}$.
    
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