Similar triangles: shadows and scale: Class 10 practice
At the same time of day, an object and its shadow form a triangle similar to any other object and its shadow, so height/shadow is the same for both.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Ratio and proportion
- Similarity
The idea behind similar triangles: shadows and scale
At the same time of day, an object and its shadow form a triangle similar to any other object and its shadow, so height/shadow is the same for both.
Step-by-step method
- Write height/shadow for the known object.
- Set it equal to height/shadow for the unknown.
- Solve and give units.
Worked example 1 (Basic)
A tree 11 m tall casts a 66 m shadow. How long is the shadow of a 1 m pole at the same time?
- 11/66 = 1/x
- x = 6 m
- Answer: 6 m
Worked example 2 (Standard)
A 4.5 m pole casts a 1 m shadow. At the same time a tower casts a 14 m shadow. Find the tower's height.
- 4.5/1 = H/14
- H = 63 m
- Answer: 63 m
Worked example 3 (Challenge)
Two similar triangles have sides 3, 6, 8 cm and the larger has perimeter 136 cm. Find its sides.
- Scale factor = 8
- Sides: 24, 48, 64 cm
- Answer: 24, 48, 64 cm
Common mistakes and misconceptions
- Mixing heights and shadows in the ratio
- Mixing units
Practice questions
- (Basic) A tree 21 m tall casts a 18 m shadow. How long is the shadow of a 3.5 m pole at the same time?
- (Basic) A tree 56 m tall casts a 84 m shadow. How long is the shadow of a 4 m pole at the same time?
- (Standard) A 2.5 m pole casts a 2 m shadow. At the same time a tower casts a 16 m shadow. Find the tower's height.
- (Standard) A 1 m pole casts a 5 m shadow. At the same time a tower casts a 65 m shadow. Find the tower's height.
- (Challenge) Two similar triangles have sides 9, 5, 7 cm and the larger has perimeter 252 cm. Find its sides.
- (Challenge) Two similar triangles have sides 4, 3, 4 cm and the larger has perimeter 165 cm. Find its sides.
Answer key with full working
- Q1: 21/18 = 3.5/x → x = 3 m → Answer: 3 m
- Q2: 56/84 = 4/x → x = 6 m → Answer: 6 m
- Q3: 2.5/2 = H/16 → H = 20 m → Answer: 20 m
- Q4: 1/5 = H/65 → H = 13 m → Answer: 13 m
- Q5: Scale factor = 12 → Sides: 108, 60, 84 cm → Answer: 108, 60, 84 cm
- Q6: Scale factor = 15 → Sides: 60, 45, 60 cm → Answer: 60, 45, 60 cm
Syllabus note
This skill is listed under "Triangles" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is similar triangles: shadows and scale in?
"Triangles", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.