Brendon has a small garden in his backyard that is already fenced. He wants to have a garden gate so that he can keep the dogs out of his garden. An example of the garden gate that Brendon wants to put up, is illustrated in the photograph below. Read the information below to answer the questions that follow. The garden gate will have 1 post on each side which will support the gate. Each post will be 0.4 m below the ground and 6 cm above the height of the gate. The height of the vertical planks is 1.3 m and has a width of 110 mm. At the bottom of the gate is a clearance gap above the ground. The gaps between each vertical plank are 3 cm. He will fit 2 horizontal planks and 1 diagonal plank to which the vertical planks will be attached. The gate is 126 cm wide. You may use the formula: (Length of diagonal plank)² = (Vertical height)² + (Width of gate)² 2.1.1 Determine the length of each post in centimeters. 2.1.2 Why must there be a clearance gap at the bottom of the gate? 2.1.3 If the horizontal planks are placed 18 cm from the bottom and top of the vertical planks, determine the length of the diagonal plank in meters. 2.1.4 You are going to assist Brendon in the project. Give a detailed description of how you would go about in doing this, using the given information.

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Brendon has a small garden in his backyard that is already fenced - NSC Mathematical Literacy - Question 2 - 2016 - Paper 2

Question 2

Brendon has a small garden in his backyard that is already fenced. He wants to have a garden gate so that he can keep the dogs out of his garden. An example of the g... show full transcript

Worked Solution & Example Answer:Brendon has a small garden in his backyard that is already fenced - NSC Mathematical Literacy - Question 2 - 2016 - Paper 2

Step 1

Determine the length of each post in centimeters.

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Answer

To determine the length of each post, we need to sum the below measurements:

Depth below the ground: 0.4 m (which is 40 cm)
Clearance gap above the ground: 8 cm
Height of the gate: 130 cm (1.3 m)
Additional height above the gate: 6 cm

The total length of each post can be calculated as:

$ext{Total Length} = 40 ext{ cm} + 8 ext{ cm} + 130 ext{ cm} + 6 ext{ cm} = 184 ext{ cm}$

Step 2

Why must there be a clearance gap at the bottom of the gate?

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Answer

A clearance gap at the bottom of the gate is essential to avoid obstruction. This gap allows for the gate to open and close freely without getting stuck on the ground or any debris, ensuring that the gate operates smoothly.

Step 3

If the horizontal planks are placed 18 cm from the bottom and top of the vertical planks, determine the length of the diagonal plank in meters.

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Answer

The vertical height of the diagonal plank can be determined as:

$ext{Vertical height} = ext{Height of vertical planks} - ( ext{Distance from bottom} + ext{Distance from top})$

Substituting the values, we have: $ext{Vertical height} = 130 ext{ cm} - (18 ext{ cm} + 18 ext{ cm}) = 130 ext{ cm} - 36 ext{ cm} = 94 ext{ cm}$

Next, we can use the formula to find the length of the diagonal plank:

$ext{Length of diagonal plank}^2 = ( ext{Vertical height})^2 + ( ext{Width of gate})^2$ $ext{Width of gate} = 126 ext{ cm}$

Now substituting the values: $ext{Length of diagonal plank}^2 = (94 ext{ cm})^2 + (126 ext{ cm})^2$

Calculating: $ext{Length of diagonal plank}^2 = 8836 + 15876 = 24712$

Taking the square root gives: $ext{Length of diagonal plank} = ext{sqrt}(24712) ext{ cm} ext{ or } 157.20 ext{ cm}$

Therefore, the length of the diagonal plank is approximately 1.57 m.

Step 4

You are going to assist Brendon in the project. Give a detailed description of how you would go about in doing this, using the given information.

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Answer

To assist Brendon in constructing the garden gate, I would follow these steps:

Gather Materials: Collect all necessary materials including wooden posts, horizontal and vertical planks, hinges, screws, and tools for digging and assembly.
Dig Holes for Posts: Use a post hole digger to create holes at each side of the gate location that are deep enough to accommodate the posts below the ground level, ensuring stability.
Plant the Poles: Place the posts into the holes and ensure they are vertical and secure by filling the holes with soil or concrete mix.
Attach Horizontal and Diagonal Planks: Cut the horizontal planks to the appropriate length and attach them between the vertical posts using screws. The placement should be 18 cm from the bottom and top of the vertical posts.
Attach Vertical Planks: Once the horizontal planks are secured, attach the vertical planks to them and ensure they are evenly spaced, with gaps of 3 cm between each plank.
Attach the Gate: Finally, attach the gate to the posts using hinges, ensuring that there is enough clearance at the bottom for it to open and close freely.

This structured approach ensures that the gate is built efficiently and effectively.

Brendon has a small garden in his backyard that is already fenced - NSC Mathematical Literacy - Question 2 - 2016 - Paper 2

Worked Solution & Example Answer:Brendon has a small garden in his backyard that is already fenced - NSC Mathematical Literacy - Question 2 - 2016 - Paper 2

Determine the length of each post in centimeters.

Why must there be a clearance gap at the bottom of the gate?

If the horizontal planks are placed 18 cm from the bottom and top of the vertical planks, determine the length of the diagonal plank in meters.

You are going to assist Brendon in the project. Give a detailed description of how you would go about in doing this, using the given information.

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