Question

Maria plans to use fencing to build an enclosure or enclosures for her two horses. A single enclosure would be square shaped and require an area of 2,025 ft2. Two individual adjacent enclosures would be rectangular, with dimensions 20 ft by 40 ft with a 40 ft divider between the two enclosures.

Which statement explains the design Maria should choose to minimize her costs?

a The singular enclosure would minimize cost because it requires 180 feet of fencing.
b The singular enclosure would minimize cost because it has the smallest area.
c The two individual enclosures would minimize cost because they require 200 feet of fencing.
d The two individual enclosures would minimize cost because they have the largest area.


The answer is A

Answer 1

The answer is A

Explanation:

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Answer 2

step 1
find the perimeter of a single enclosure
perimeter of a square=4*b
where b is the long side of a square
area square=b²
area square=2025 ft²
b²=2025-------> b=√2025-----> b=45 ft
so
perimeter=4*45-------> 180 ft

step 2
find the perimeter of a two individual enclosure
perimeter=4*20+3*40------> 200 ft
area=20*40*2------> 1600 ft²

therefore
fencing singular enclosure < fencing two individual enclosure
180 ft < 200 ft

area singular enclosure > area two individual enclosure
2025 ft² > 1600 ft²

the answer is the option
a The singular enclosure would minimize cost because it requires 180 feet of fencing.