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 8 cm 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 find the length of each post, we need to account for the height of the gate, the clearance gap, and the portion of the post that goes underground. Using the formula:

Length of post = height above ground + clearance gap + height of gate + height underground.

Given:

Height above ground = 0.06 m (6 cm)
Height of gate = 1.3 m
Clearance gap = 0.08 m (8 cm)
Height underground = 0.4 m

Substituting these values:

Length of post = 0.4 + 0.08 + 1.3 + 0.06 = 1.84 m or 184 cm.

Step 2

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

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Answer

The clearance gap at the bottom of the gate is essential to ensure that the gate can open and close freely without obstruction from the ground or any debris. This prevents the gate from getting stuck and allows for proper functioning over time, especially considering changes due to weather conditions such as soil expansion or settling.

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

To determine the length of the diagonal plank, we first need to find the vertical height:

Vertical height = total height of vertical plank - (distance from bottom to horizontal plank + distance from top to horizontal plank).
The total height of the vertical plank = 1.3 m or 130 cm.
The distance from the bottom to the horizontal plank = 18 cm and from the top is also 18 cm.

So, the vertical height becomes:

Vertical height = 130 - (18 + 18) = 130 - 36 = 94 cm.

Using the formula provided:

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

Substituting in the values:

Width of gate = 126 cm = 1.26 m.

Then:

Length of diagonal plank = $ext{Length of diagonal plank}^2 = 94^2 + 126^2 = 8836 + 15876 = 24712$ .

Taking the square root:

Length of diagonal plank = $ext{Length of diagonal plank} = ext{√(24712)} = 157.2 ext{ cm} = 1.572 ext{ m}$ .

Step 4

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

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Answer

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

Gather Materials: Collect all necessary materials including vertical planks, horizontal planks, screws, hinges, and the posts.
Preparation of Site: Mark the positions where the posts will be installed. Ensure the area is clear of debris.
Digging Holes: Dig holes deep enough to securely fit the posts, considering the depth that will be underground (0.4 m).
Install Posts: Place the posts in the dug holes, ensuring they are level and straight, and then fill the holes back with soil to secure them.
Attach Horizontal Planks: Use screws to attach the horizontal planks to the posts, ensuring they are 18 cm from both the bottom and top of the vertical planks.
Attach Vertical Planks: Secure the vertical planks to the horizontal planks using screws, maintaining equal gaps of 3 cm between each vertical plank.
Attach Diagonal Plank: Finally, attach the diagonal plank from the bottom of one vertical plank to a suitable position on the opposite plank to provide stability.
Install Gate with Hinges: Attach the gate to the posts using hinges, ensuring that the 8 cm gap is maintained at the bottom for clearance.
Final Adjustments: Test the gate to ensure smooth operation and make any necessary adjustments.

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 doing this, using the given information.

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