1 Scale and lengths / 4 pts
A map uses the scale 1 cm : 6 m.
- A path measures 3.5 cm on the map. Find its actual length.
- A pool is 90 m long. How long is it on the map?
- Write the scale as a ratio with the same unit on both sides.
2 Two rectangles / 4 pts
Rectangle ABCD is 4 cm by 7 cm. Rectangle A′B′C′D′ is a scale drawing of ABCD with a short side of 10 cm.
- Find the scale factor.
- Find the long side of A′B′C′D′.
- Find both perimeters.
- Find both areas and compare them.
3 Distances on a map / 3 pts
A road map has the scale 1 in : 12 mi.
- Two towns are 3.25 in apart on the map. What is the actual distance?
- A trip is 78 mi long. How many inches does it measure on the map?
4 A living room plan / 4 pts
A floor plan uses the scale 1 cm : 2 ft. The living room is a rectangle 7 cm by 5 cm on the plan.
- Find the actual dimensions.
- Find the actual area.
- Find the area on the plan.
- Show that the two areas are related by the square of the scale.
5 Similar triangles / 3 pts
Triangle ABC has sides 5, 12, and 13. Triangle DEF is similar to it, and its shortest side is 15.
- Find the scale factor.
- Find the other two sides of DEF.
- Triangle ABC has area 30. Find the area of DEF.
6 True or false? / 2 pts
Say whether each statement is true or false and justify.
- If a drawing uses a scale factor of 3, the actual area is 3 times the drawing area.
- In a scale drawing, the angles are the same as in the original.
Test yourself: quick challenge for Grade 7
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