The dimensions of the map are 8 feet × 4 feet
Step-by-step explanation:
Step 1; It is given that the perimeter of the map is 24 feet while the area is 32 square feet. The map is in the shape of a rectangle so we need to calculate its length and its width of this rectangle. The area of any particular rectangle is given by the multiplication of its length with width. The perimeter is given by double the value of the sum of its length and width.
Step 2; Equating these we get
Perimeter = 2 (l + w) = 24 feet
Area = l × w = 32 feet.
From the perimeter formula, (l + w) = = 12
So we have (l + w) = 12 while l × w = 32.
Step 3; Possible values of l and w are
(1 ,11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6), (7, 5), (8, 4), (9, 3), (10, 2) and (11, 1).
Out of these possibilities only (4, 8) and (8, 4) give a product of 32 but since l is greater than w we have the value of l as 8 feet while w is 4 feet.