Question

When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square.
The total length of each row of bookshelves will be "4" /"5" of the length of the storage space.
Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points)

Write a function that expresses f(x). (10 points)


 
Graph the function. (10 points)

Answer 1

Area = 8,100 square feet
area of a square = a²
8,100 square feet = a²
√8,100 square feet = √a²
90 feet = a

total length each row of bookshelf is 4/5 of the length of the storage space.

90 feet * 4/5 = (90*4)/5 = 360/5 = 72 feet.

Area = (72 ft)²
Area = 5,184 square feet.