Applications of Similarity

Measuring what you cannot reach.

12 problems · about 21 minutes · G-SRT.B.5

NameDate

Figure — use these to answer the problems

A scale drawing is a dilation. Change the factor to see the real size a drawing stands for.

Before: 3

After: 12

4 × 3 = 12

Drawn length3

Scale factor, top4

Scale factor, bottom1

Figure 1

Straightforward practice. Get the method working first.

5 problems

A 2 m post casts a 3 m shadow. A tower casts a 30 m shadow. Height in metres?
Answer
2
At a scale of 1 to 500, what is the ratio of areas?
- 1 to 250000, the square of the length ratio.
- 1 to 500, the same as lengths.
A 3 m post casts a 4 m shadow. A tree casts a 20 m shadow. Tree height in metres?
Answer
A 2 m post casts a 5 m shadow. A building casts a 40 m shadow. Height in metres?
Answer
Scale 1 to 200. A drawn 5 cm stands for how many centimetres?
Answer

The same ideas with more to keep track of.

3 problems

Scale 1 to 50. A real 600 cm is drawn as how many centimetres?
Answer
At scale 1 to 100, areas are in what ratio? Enter the second number.
Answer
A 1 m stick casts a 2 m shadow. A pole casts a 14 m shadow. Height in metres?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Put the shadow method in order.
Write 1 to 4 in the boxes to put these in order.
- Note that the sun is at the same angle for both objects.
- Conclude the two triangles are similar by AA.
- Set the height to shadow ratios equal.
- Cross-multiply and solve for the unknown height.
Scale 1 to 25. A real 300 cm is drawn as how many centimetres?
Answer
The Tree
A 2 m post casts a 3 m shadow. A tree casts a 21 m shadow. How tall is the tree, in metres?
Answerm
The Map
A map has scale 1 to 500. A drawn length of 4 cm stands for how many centimetres?
Answer