A winter recreational rental company is fencing in a new storage area. They have two options. They can set it up at the back corner of the property and fence it in on four sides. Or, they can attach it to the back of their building and fence it in on three sides. The rental company has decided that the storage area needs to be 100 m2 if it is in the back corner or 98 m2 if it is attached to the back of the building. Determine the optimal design for each situation

The optimal side length for a storage area at the back corner of the property fenced on four sides and having an area of 100 m² is 10 meters

The optimal side length for a storage area attached to the back of their building fenced on three sides and having an area of 98 m² is 7·√2 m

Step-by-step explanation:

The optimal design to conserve building material will be to build the storage area to have equal sides which gives square shaped storage area

For a storage area at the back corner of the property fenced on four sides and having an area of 100 m², we have;

Storage area size = 100 m²

The number of sides = 4

The dimension of each side = Equal sides, s₁

Therefore we have;

s₁ × s₁ = 100

s₁² = 100

s₁ = √100 = 10 m

The side length = 10 m

For a storage area attached to the back of their building fenced on three sides and having an area of 98 m², we have;

Storage area size = 98 m²

The number of sides = 4

The dimension of each side = Equal sides, s₂

Therefore we have;

s₂ × s₂ = 98

s₂² = 98

s₂ = √98= 7·√2 m

The side length = 7·√2 m