Answer:
3.41 feet
Step-by-step explanation:
Area = Length × Breath
Area of the rectangular lawn = 100 × 50
= 5000 feet²
The sidewalk must occupy an area no more than 10% of the total lawn area.
So, the area of the sidewalk would be not more than = 10% × 5000
= 0.10 × 5000
= 500 feet²
Let the width of the sidewalk = x feet
area of the side walk = (L×W of the long way) + ((L-x)×W of the short way)
(100 × x) + ((50 - x) × x) < 500
100x + (50-x)(x) < 500
-x² + 150x < 500
-x² + 150x = 500
-x² + 150x - 500 = 0
By using quadratic formula
or 
x = 3.41089 ≈ 3.41 feet or x = 146.58
Therefore, width of the sidewalk would be 3.41 feet.
Answer:
d
Step-by-step explanation:
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For a better understanding of the answer given here, please go through the diagram in the attached file.
The diagram assumes that the base of the hexagonal pyramid is an exact fit (has same dimensions as the face of the hexagonal prism).
As can be seen from the diagram, the common vertices are A,B,C,D,E,F which are 6 in number.
The bottom vertices are G,H,I,J,K,L, which, again are 6 in number.
The Apex of the pyramid, P is one more vertex.
Thus, the total number of vertices in a Hexagonal pyramid is located on top of a hexagonal prism will be the sum of all these vertices and thus will be:
6+6+1=13
