Jacob's little brother thinks that he could design a better lion enclosure than the one he sees at the zoo. He makes a drawing of his new and improved enclosure where every inch represents 25 feet. In his drawing the length of the rectangle is 7 ¼ inches. What is the actual length of the lion enclosure? The diagonal of the rectangle in his drawing is 10 ½ inches. What is the width of the enclosure in feet? What is the area of the enclosure in square feet?

Step-by-step explanation:

Length

1 inch = 25 feet

7 1/4 inches = x feet

1 * x = 25 * 7 1/4

x = 25 * 7.25

Length = 181.25 feet

The length is 181.25

hypotenuse length

The diagonal = 10 1/2 inches

The diagonal = 10.5 inches

hypotenuse = 10.5 * 25 = 262.5 feet

Width

L^2 + W^2 = Diagonal^2

181.25² + W² = 262.5²

32851.5625 + W²  =  68906.25   Subtract 32851.5625 from both sides

W² =  68906.25 - 32851.5625

W^2 = 36054.6875                       Take the square root of both sides

W = 189.88

Area

Area = L * W

Area = 181.25 * 189.88

Area = 34415.88 square feet.