Question

Sebastian is drawing a map of his local park. The actual park is a rectangle that is 300 feet long and 240 feet wide. Sebastian needs his drawing to fit on his paper, so he decides to make the long side 10 inches. What scale is Sebastian using? What is the area of Sebastian's drawing in square inches?

Answer 1

Sebastian is using a scale of 1 inch to 30 feet for his drawing. The area of Sebastian's drawing in square inches is 80 square inches.

Step-by-step explanation:

Sebastian is using a scale to represent the actual dimensions of a park on his drawing. To find the scale factor, we compare the drawing's dimensions to the actual dimensions. The actual length of the park is 300 feet, and on Sebastian's map, it is 10 inches. If we convert feet to inches, knowing that one foot is equal to 12 inches, the actual length in inches is 300 feet x 12 inches/foot = 3600 inches. So, the scale is 10 inches on the drawing to 3600 inches in reality, which reduces to 1 inch to 360 inches, or 1 inch to 30 feet.

Now, to find the width scale for the drawing, we use the same method. The actual width is 240 feet, converted to inches is 240 feet x 12 inches/foot = 2880 inches. Taking the drawing width to be in proportion with the length, we must find the number that, when multiplied by the scale factor, gives us the drawing width. If 1 inch on the drawing represents 30 feet then to find the drawing width in inches: 240 feet / 30 feet/inch = 8 inches. Now we have a scale of 1 inch to 30 feet for both length and width.

To calculate the area of Sebastian's drawing, we multiply the drawing's length by its width. With a length of 10 inches and a width of 8 inches: Area = 10 inches x 8 inches = 80 square inches.

Answer 2

the ratio of the park's length and width is 300/240=5/4
if he takes the length as 10in then the width should be 8in,
so it's area should be 80in²