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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.
Answer
To find the length of each post, we add the lengths: the part below the ground (0.4 m), clearance gap (8 cm), height of the gate (1.3 m), and the part above the gate (6 cm). First, convert everything into centimeters:
- 0.4 m = 40 cm
- Height of the gate = 130 cm
- Clearance gap = 8 cm
- Part above the gate = 6 cm
Now, summing these values:
Length of post = 40 cm + 8 cm + 130 cm + 6 cm = 184 cm.
Step 2
Why must there be a clearance gap at the bottom of the gate?
Answer
The clearance gap at the bottom of the gate is essential to ensure that the gate can open and close freely without any obstructions. This prevents it from getting stuck on the ground or any debris, ensuring smooth functionality.
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.
Answer
To find the vertical height of the diagonal plank, we calculate:
Vertical height = Height of vertical plank - (height of the bottom horizontal plank) - (height of the top horizontal plank)
Vertical height = 130 cm - (18 cm × 2) = 130 cm - 36 cm = 94 cm.
Using the provided formula for the length of the diagonal plank:
Length of diagonal plank² = (Vertical height)² + (Width of gate)²
Substituting the values into the formula:
Length of diagonal plank² = (94 cm)² + (126 cm)² Length of diagonal plank² = 8836 + 15876 = 24712.
Now, to obtain the length, take the square root: Length of diagonal plank = √24712 cm = 157.200... cm = 1.572 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.
Answer
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Dig the holes for the posts: Identify the locations for the gate posts and dig holes deep enough to accommodate the 0.4 m below-ground portion.
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Plant the poles in the holes: Position the poles in the dug holes and ensure they are vertically aligned.
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Attach the horizontal and diagonal planks with screws: Start with the horizontal planks at 18 cm from both the top and bottom, securing them in place.
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Attach the vertical planks to the horizontal and diagonal planks with screws: Position the vertical planks evenly between the horizontal ones, leaving a 3 cm gap.
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Attach the gate to the posts with hinges: Finally, mount the gate onto the framework of vertical and horizontal planks ensuring that it can swing open and close properly.