Students are painting the backdrop for the school play. The backdrop is 15 feet wide and 10 feet high. Every 16 inches on the scale drawing represents 5 feet on the backdrop. What is the area of the scale drawing?
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1,536 inches
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1536
Scale = 16in/5ft = 3.2 in/ft.
Width = 15Ft * 3.2in/ft. = 48 in.
Height = 10ft * 3.2in/ft. = 32 in.
Area = 48 * 32 = Square inches.
A sand box is 1 1/3 ft. tall and 1 5/8 ft. wide, and 4 1/2 ft. long, how many cubic ft. will it hold?
To find the area of the scale drawing, we need to first determine the dimensions of the scale drawing.
Given that every 16 inches on the scale represents 5 feet on the actual backdrop, we can set up a proportion to find the width and height of the scale drawing:
16 inches / 5 feet = x inches / 15 feet (width of the actual backdrop)
Simplifying the proportion, we get:
16/5 = x/15
Cross-multiplying, we find:
5x = 16 * 15
Dividing both sides by 5, we get:
x = (16 * 15) / 5
x = 48 inches
So, the width of the scale drawing is 48 inches.
We can follow the same steps to find the height:
16 inches / 5 feet = y inches / 10 feet (height of the actual backdrop)
Simplifying and solving for y, we find:
y = (16 * 10) / 5
y = 32 inches
Thus, the height of the scale drawing is 32 inches.
To find the area of the scale drawing, we multiply the width and height:
Area = width * height
= 48 inches * 32 inches
= 1536 square inches.
Therefore, the area of the scale drawing is 1536 square inches.