An Architect's Day

A total of 90 feet of fencing is to be used for a garden besides the house. What is the maximum area the given fence in feet may cover in meters?

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The owner wishes to add a small shed within the garden for storing tools. The perimeter he proposes is 40 feet. What are the dimensions needed for the largest area of the shed possible in meters?

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Within the garden, the client also wishes to have an enclosure for sensitive crops. He wishes to use an area of 97 square feet. Three sides will use bricks that cost 0.5$ while one side will use stone that costs 0.2$. Find the dimensions in meters that will cost the least.

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For the interior planning, the client proposed a kitchen area of 140 square feet. What is the perimeter covered by the largest possible dimensions in meters?

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A rectangular living room will have a total area of 33 square meters and will have 15 cm trimmed off of all sides for the walls except for the southern side which will have 20 cm trimmed off instead. What dimensions will give the largest area for the living room?

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Given the surface area of a guest room with 215 square feet, find the largest possible volume of the room in cubic meters without taking the ceiling into account.

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The perimeter of the rectangular lot bought by the client is 248 feet. Because the client bought the largest possible area, find the area of the land in meters.

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Inside the area of the land lies the rectangular outline of the house itself, possessing a volume of 2800 cubic feet. If the dimensions were to be the minimum, what would the dimensions be in feet? Note that the roof is not considered within the outline.

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In relation to the location of the client's house, he wishes to know the fastest way for his children to reach their house after school. The house is located 12 miles north from the main road. The main road spans straight for 26 miles from that point up to the school's location. Additionally, there's a nearby private sector that allows buses pass through. The buses that pass through the private sector move at a speed of 40 mph while the jeeps that pass through the main road move at a speed of 60 mph. At what distance should his children take a bus to minimize the time reaching their house?

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