Introduction: The school wants students in your grade to design and develop their own birdhouses that can be hung on trees around campus. They want the structure of the house to be built out of at most 5 wooden beams and have a similar shape as shown in Diagram 1. The school only has a limited amount of wood that can be used for the construction of the structure of the houses. For that reason, the school has decided to hold a design competition where the house designs that use the least amount of wood would get priority in the selection so that the greatest number of houses could be built.
Rules of the competition: The school is using Diagram 1 for the basis of the competition, so the following needs to be considered:
There are at most 5 beams that can be used to make the birdhouse (shown in yellow).
The four sloping beams all have the same length.
The dimensions for the rectangular base of the birdhouse have to be 60 cm long, 50cm wide.
The distance from the rectangular base and the horizontal beam must be 20 cm.
The distance x from the sides of the house to where the pair of the sloping beams meet should make it so that the least amount of wood is used.
Task: In order for your birdhouse to have the best chance of being accepted you must write a preliminary measurements proposal that takes the rules of the competition into account. In the proposal you need to:
Find the value x, so that the distance from the side of the house to where the two sloping beams meet uses the minimal amount of wood in the construction of the birdhouse.
Trial and improvement may be used to show how you have come to your value for x.
Explain, and justify with reasons, how accurate you believe your answer for x is and why there may be some inaccuracies.
Explain, and justify with reasons, why you believe that this value of x would use the least amount of wood in the construction of the house.
Communicating your report: Make sure that in your report that you do the following to communicate properly (all of this is graded against Criterion C):
Use appropriate mathematical language and notation consistently.
Show all your working out in an organized and logical way.
Explain your thinking and answers in such a way that they are clear and coherent.
Use at least 4 of calculations, diagrams, tables, explanations, etc. in such a way so that they reinforce each other.
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What did Mahatma Gandhi urge people during the national movement?
Answer:
During the national movement Mahatma Gandhi urged people to boycott imported textiles and use hand-spun and hand-woven cloth.
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