A new ice cream shop draws a design for its shop sign that is 4 inches wide and 9 inches long. A sign building company builds a sign of the design using a scale factor of 15.
Part A: What are the dimensions of the sign, in feet? Show every step of your work. (2 points)
Part B: What is the area of the sign, in square feet? Show every step of your work. (2 points)
Part A:
To find the dimensions of the sign in feet, we need to convert the measurements from inches to feet.
Given: Width = 4 inches, Length = 9 inches
Converting the width from inches to feet:
4 inches * (1 foot / 12 inches) = 4/12 = 1/3 feet
Converting the length from inches to feet:
9 inches * (1 foot / 12 inches) = 9/12 = 3/4 feet
Therefore, the dimensions of the sign are 1/3 feet wide and 3/4 feet long.
Part B:
To find the area of the sign in square feet, we need to multiply the width and length of the sign in feet.
Area = Width * Length
Area = (1/3 feet) * (3/4 feet)
Area = (3/12) * (3/4) = 9/48 = 3/16 square feet
Therefore, the area of the sign is 3/16 square feet.