Problem 1: Map distance
A map of Texas uses the scale \(1\text{ in}=20\text{ mi}\). Dallas and Waco are \(3.5\text{ in}\) apart on the map. Find the actual distance.
Problem 2: City map
A city map uses the scale \(1\text{ in}=12\text{ mi}\). Riverton and Oakdale are \(6.5\text{ in}\) apart on the map. Find the actual distance between the two towns.
Problem 3: Actual to drawing
A scale drawing uses \(1\text{ in}=4\text{ ft}\). A wall is \(18\text{ ft}\) long. How long is the wall in the drawing?
Problem 4: Furniture plan
Priya draws a floor plan with the scale \(1\text{ in}=5\text{ ft}\). Her couch is \(7\text{ ft}\) long. How long is the couch on the plan?
Problem 5: Find the scale
On a scale drawing, a fence that is actually \(30\text{ ft}\) long measures \(6\text{ in}\). Write the scale as \(1\text{ in}=\) ___ \(\text{ft}\).
Problem 6: Model airplane
A wing of a model airplane is \(4\text{ in}\) long. The wing of the real airplane is \(28\text{ ft}\) long. Write the scale as \(1\text{ in}=\) ___ \(\text{ft}\).
Problem 7: Scale as a ratio
A model uses the scale \(1\text{ in}=3\text{ ft}\). Write the scale as a ratio with no units, using the same unit for both lengths.
Problem 8: Yards to a ratio
A map of a golf course uses the scale \(1\text{ in}=10\text{ yd}\). Write the scale as a ratio with no units, using the same unit for both lengths.
Problem 9: Half-inch scale
A deck plan uses the scale \(\frac{1}{2}\text{ in}=3\text{ ft}\). On the plan the deck is \(5\text{ in}\) long and \(3\text{ in}\) wide. Find the actual length and width of the deck.
Problem 10: Blueprint of a room
On a blueprint with scale \(1\text{ in}=4\text{ ft}\), a room measures \(9\text{ in}\) by \(6\text{ in}\). Find the actual dimensions and the actual area of the floor.
Problem 11: Classroom floor
The plan of a classroom is a rectangle \(7\text{ in}\) by \(5\text{ in}\). The scale is \(1\text{ in}=3\text{ ft}\). Find the actual length, width and area of the classroom floor.
Problem 12: Area from a drawing
A patio is drawn as a \(5\text{ in}\) by \(2\text{ in}\) rectangle with the scale \(1\text{ in}=3\text{ ft}\). Find the actual area of the patio. How many times as large is the actual area as the drawing area?
Problem 13: Scale from area
A stage is drawn as a rectangle \(3\text{ in}\) by \(2\text{ in}\). The actual stage has an area of \(864\text{ ft}^{2}\). Find the scale of the drawing as \(1\text{ in}=\) ___ \(\text{ft}\). Then find the actual length and width.
Problem 14: A new scale
A rectangle is drawn \(4\text{ in}\) by \(2.5\text{ in}\) with the scale \(1\text{ in}=6\text{ ft}\). Find its dimensions in a new drawing that uses \(1\text{ in}=3\text{ ft}\).
Problem 15: Redraw a triangle
A triangular garden is drawn as a right triangle with sides \(1.5\text{ in}\), \(2\text{ in}\) and \(2.5\text{ in}\) at the scale \(1\text{ in}=20\text{ ft}\). (a) Find the actual side lengths. (b) Find the side lengths of a new drawing at the scale \(1\text{ in}=10\text{ ft}\). (c) Find the perimeter of the new drawing.
Problem 16: Playground plan
A playground plan uses \(1\text{ in}=8\text{ ft}\). The sandbox is a rectangle \(1.5\text{ in}\) by \(1\text{ in}\) on the plan. Find the actual perimeter and area of the sandbox.
Problem 17: Soccer field
A youth soccer field is \(120\text{ yd}\) by \(60\text{ yd}\). Ethan draws it with the scale \(1\text{ in}=20\text{ yd}\) on a sheet of paper that is \(8.5\text{ in}\) by \(11\text{ in}\). Find the dimensions of his drawing. Does it fit on the paper?
Problem 18: New floor
The plan of a living room is a rectangle \(4\text{ in}\) by \(3\text{ in}\) with the scale \(1\text{ in}=5\text{ ft}\). Flooring costs $2.50 per square foot. Find the actual area of the room and the cost to cover the whole floor.
Problem 19: Road trip
On a map with scale \(1\text{ in}=15\text{ mi}\), Maya’s route from home to a rest stop measures \(2.4\text{ in}\) and from the rest stop to the lake measures \(3.1\text{ in}\). Find the total actual distance. How long does the trip take at an average speed of \(55\text{ mph}\)?
Problem 20: Park map on paper
A park is \(450\text{ ft}\) by \(270\text{ ft}\). Mei wants to draw it on a sheet of paper with a drawing area of \(9\text{ in}\) by \(6.5\text{ in}\). She can choose \(1\text{ in}=40\text{ ft}\), \(1\text{ in}=50\text{ ft}\) or \(1\text{ in}=60\text{ ft}\). Which scale gives the largest drawing that still fits? Give the drawing dimensions.
See every chapter on the Grade 7 math page.