In this discussion board one was asked to calculate the formula for the area of
ID: 3103609 • Letter: I
Question
In this discussion board one was asked to calculate the formula for the area of the garage that John wanted to renovate and attach it to his house. John worked with a contractor and was informed that the area of his new garage will be limited to the cost of the materials he needed to purchase. The total length of the three walls that he could afford was 68 feet. Unfortunately, the kitchen wall would serve as the fourth wall. However John wanted to place two big cars into this garage and wanted it to be the biggest possible area under the contractor’s constraints.After calculating the formula for the area of the garage, one was informed to choose two dimensions to plug into the formula of choice and answer the following questions:
• What areas result? If you get a negative area, your dimension was too large, so select another.
• Next, use the vertex formula to find the dimension that produces the maximum area of the garage.
• Find the maximum area.
• Will the garage be large enough to accommodate the two cars?
• How does the length of the kitchen wall affect the structure of the garage?
Explanation / Answer
The garage will be the shape of a rectangle. That means opposite sides will have the same length. Since the kitchen forms one wall, the wall across from the kitchen has to be the same length as the kitchen wall. The two side walls will have to be the same size as each other also in order to have a rectangle. The area of the rectangle is length * width. For this garage, given the constraints of the kitchen wall, this means that the area of the garage is 2*kitchen wall + 2*the length of the side walls. This means that you only have one choice for the length of the side walls. That would be:
side wall = (68 – length of kitchen wall)/2
This makes the area of the garage:
Length of the kitchen wall * length of side wall
If they do not give you the length of the kitchen wall, you cannot figure out the actual area or if it will fit two cars.
Hope this helps some.
Kitchen wall
s s
i i
d d
e e
w w
a a
l l
l l
Garage wall
Kitchen wall
s s
i i
d d
e e
w w
a a
l l
l l
Garage wall
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.