Problem 3 - Edging the path
Problem 3 is all about figuring out measurements and calculating costs in a gardening problem.
Maths teacher Chris Smith and pupils from Grange Academy are here to explain.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
CHRIS This challenge is all about figuring out measurements and calculating the cost involved in a gardening problem.
Maryam and Blair are doing a bit of landscaping on a square lawn with an area for four hundred square metres. It's surrounded by a path that is two metres wide.
They need to put edging stones on both sides of the path to strengthen it.
Each edging stone is fifty centimetres long and costs twelve pounds.
How much do Maryam and Blair have to pay for the edging stones?
Right, you've got a square lawn, right, grass in the middle, and then all the way round, you've got this edging. We鈥檙e gonna try and work out how much edging there is and work out how much it鈥檚 gonna cost us to put that edging in place.
PUPILS
Try drawing out the lawn yourself.
Can you work out the length of each side of the lawn first?
Don't forget they're putting stones on both sides of the path. Not just one.
Remember, you need to consider the length of the stones.
Give it a go.
So here's the challenge:
A square lawn of area 400 m虏 is surrounded by a path that is 2 m wide.
Maryam and Blair need to put edging stones on both sides of the path to strengthen it. Each stoneis 50 cm long and costs 拢12.
How much do Maryam and Blair have to pay for the edging stones?
Need a hint?
- Try drawing out the lawn yourself.
- If we know the lawn is square and has an area of 400 m虏, can you work out the length of each side first?
- Don鈥檛 forget they are putting edging stones down on both sides of the path 鈥 not just one.
- Remember, you need to consider the length of the edging stones.
Solution
Worked out the answer? Here's how you can do it.
In this challenge, Maryam and Blair want to put edging stones along the path around their lawn.
If the lawn is square and has an area of 400 square metres. Then we know it's side is 20 metres, because the square root of 400 is 20 because 20 x 20 = 400.
If each side is 20 metres, we can multiply that by 4 sides and work out that the edging stones for the inside of the path have a total length of 20 x 4, which equals 80 metres.
What about the stones on the outer edges of the path?
The path is 2 metres wide so the outer edges of the path will be 2 metres longer at each edge of each side.
So each side is 20 + 2 + 2, which is 24 metres.
And there are four sides so the total is 24 x 4, which is 96 metres.
So the total length to be edged, is 80 metres for the inside edge and 96 metres for the outside edge, which is 176 metres.
Since each edging stone is 50 centimetres or half a metre in length. We'll need to double the total length to work out how many stones we need.
2 x 176 = 352.
Maryam and Blair need 352 edging stones.
Now, we can work out the total cost.
Each edging stone cost twelve pounds so 352 stones x 拢12 per stone is 拢4224.
Did you work it out?
In this challenge, Maryam and Blair want to put edging stones along the path around their lawn.
If the lawn is square and has an area of 400 m虏, then we know its side is 20 m because the square root of 400 is 20:
鈭400 = 20
The inside edges of the path
If each side is 20 m we can multiply that by 4 sides and work out the total length of the edging stones for the inside of the path
20 x 4 = 80 m
The inside edge of the path measures 80 metres
What about the stones on the outer edges of the path?
The path is 2 m wide so the outer edges of the path will be 2 m longer at each edge of each side.
So each side is: 20 + 2 + 2 = 24 m
And there are four sides so the total length of the outside edge is 24 x 4 = 96 m
Total length
The total length to be edged is
- 80 metres for the inside edge
- 96 metres for the outside edge
80 + 96 = 176 m
Since each edging stone is 50 cm or half a metre in length. We'll need to double the total length to work out how many stones we need.
2 x 176 = 352
Maryam and Blair need 352 edging stones.
Now, we can work out the total cost.
Each edging stone cost twelve pounds so:
352 stones x 拢12 per stone = 拢42242 m
Maryam and Blair will have to pay 拢4224 for the edging stones.
Maths Week Scotland 2022. list
Try out all the daily challenges from Maths Week Scotland 2022.
Maths Week Scotland 2021. list
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Maths Week Scotland 2020. list
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