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A tetrahedron is a triangular pyramid. It has four triangular faces and four vertices.
In the question, we are told that the length of the edges are all equal = 20m and the length from one corner to the center of the base = 11.5m
We sketch a diagram of a tetrahedron with the given measurement as shown below
To find the height, we will use the Pythagoras theorem
20² = h² + 11.5²
h² = 20² - 11.5²
h² = 267.75
h = √267.75
h = 16.36 (rounded to two decimal places)
In the question, we are told that the length of the edges are all equal = 20m and the length from one corner to the center of the base = 11.5m
We sketch a diagram of a tetrahedron with the given measurement as shown below
To find the height, we will use the Pythagoras theorem
20² = h² + 11.5²
h² = 20² - 11.5²
h² = 267.75
h = √267.75
h = 16.36 (rounded to two decimal places)
Answer:
bottom side (a) = 3.36 ft
lateral side (b) = 4.68 ft
Step-by-step explanation:
We have to maximize the area of the window, subject to a constraint in the perimeter of the window.
If we defined a as the bottom side, and b as the lateral side, we have the area defined as:
The restriction is that the perimeter have to be 12 ft at most:
We can express b in function of a as:
Then, the area become:
To maximize the area, we derive and equal to zero:
Then, b is:
