Case Study Questions on Triangles Chapter 5 for Class 10 with Answers

This set of case-study questions for Chapter 6: Triangles Class 10 follows CBSE and NCERT guidelines and presents short, exam-style scenarios designed to build geometric reasoning, proof skills, and stepwise problem solving. Problems cover triangle congruence and similarity, properties of medians, altitudes and perpendicular bisectors, criteria and applications of similarity in ratio problems, exercises using the Basic Proportionality Theorem (Thales), and proofs that connect angle and side relations. Each question includes a clear, step-by-step solution and final answer keys. A downloadable PDF accompanies the pack with practice sets for quick revision, classroom worksheets for guided practice focused on improving speed and accuracy.

Solved Case Study Questions and Answers on Triangles

CBSE's case-based questions usually give you a short passage describing a real situation, sometimes with a small figure, followed by 4 - 5 questions of increasing difficulty, a couple of MCQs to check basic understanding, a short-answer question that needs a calculation, and a longer question that asks you to interpret or justify your answer.

Case Study 1:Vijay, Ajay and the Tower: Shadow Proportions

Vijay is trying to find the average height of a tower near his house. He uses the properties of similar triangles. Vijay's house is 20 m tall and casts a shadow 10 m long on the ground at a certain time of day. At that same moment, the tower casts a shadow 50 m long, and his neighbour Ajay's house casts a shadow 20 m long on the ground.

Q1 What is the height of the tower?

(a) 20 m

(b) 50 m

(c) 100 m

(d) 200 m

Q2 What is the height of Ajay's house?

(a) 30 m

(b) 40 m

(c) 50 m

(d) 20 m

Q3 When Vijay's house casts a shadow of 12 m, what will be the length of the tower's shadow?

(a) 75 m

(b) 50 m

(c) 45 m

(d) 60 m

Q4 When the tower casts a shadow of 40 m, what will be the length of the shadow of Ajay's house?

 (a) 16 m

(b) 32 m

(c) 20 m

(d) 8 m

Solution: 

Q1: Height of tower / Shadow of tower = Height of Vijay's house / Shadow of Vijay's house

⇒ Height of tower / 50 = 20 / 10

⇒ Height of tower = 2 × 50 = 100 m

Q2: Height of Ajay's house / 20 = 20 / 10

⇒ Height of Ajay's house = 2 × 20 = 40 m

Q3 : The new ratio = Height of Vijay's house / new shadow = 20/12 = 5/3

Tower's shadow × (5/3) = 100 ⇒ Tower's shadow = 100 × 3/5 = 60 m

Q4: Shadow of Ajay's house / Shadow of tower = Height of Ajay's house / Height of tower

= 40/100 = 2/5

Ajay's shadow = (40/100) × 40 = 16 m

Case Study 2: The Lamp-Post and the Walking Girl

A girl of height 90 cm walks away from the base of a lamp-post at a speed of 1.2 m/s. The lamp is 3.6 m above the ground. The girl walks for 4 seconds and then stops.

Q1 What is the girl's distance from the base of the lamp-post after 4 seconds?

(a) 1.2 m

(b) 4.8 m

(c) 6.0 m

(d) 3.6 m

Q2 What is the length of her shadow after 4 seconds?

(a) 1.0 m

(b) 1.2 m

(c) 1.6 m

(d) 2.4 m

Q3 Find the ratio AC : CE (i.e., total length from lamp base to girl's head tip : shadow)

(a) 4 : 1

(b) 2 : 1

(c) 3 : 1

(d) 4 : 3 

Solution: 

Q1 : Distance = Speed × Time = 1.2 m/s × 4 s = 4.8 m

Q2: △ABE ~ △CDE (AA), so BE/DE = AB/CD

(4.8 + x)/x = 3.6/0.9 = 4

4.8 + x = 4x ⇒ 3x = 4.8 ⇒ x = 1.6 m

Q3: AE = AB + BD + DE = 3.6 m from lamp to end isn't needed; we use:

AE/CE = BE/DE = (4.8 + 1.6)/1.6 = 6.4/1.6 = 4

So AE = 4 CE, meaning AC = AE − CE = 3CE

Therefore AC : CE = 3 : 1

Case Study 3: Two Triangular Land Plots

Two triangular land plots, Plot X and Plot Y are geometrically similar. The sides of Plot X measure 30 m, 40 m, and 50 m. The corresponding sides of Plot Y measure 15 m, 20 m, and 25 m. The area of Plot Y is 150 m².

Q1 What is the ratio of corresponding sides (Plot X : Plot Y)?

(a) 1 : 2

(b) 2 : 1

(c) 3 : 1

(d) 4 : 1

Q2 What is the ratio of the areas of Plot X to Plot Y?

(a) 2 : 1

(b) 3 : 1

(c) 4 : 1

(d) 8 : 1

Q3 Is Plot X a right-angled triangle? Which theorem applies?

(a) Yes, Converse of Pythagoras Theorem

(b) No, it is not right-angled

(c) Yes, Pythagoras Theorem

(d) Cannot be determined

Q4 What is the area of Plot X?

(a) 300 m²

(b) 450 m²

(c) 600 m²

(d) 750 m²

Solution: 

Q1: 30/15 = 40/20 = 50/25 = 2 : 1

Q2:  Area ratio = (Side ratio)² = (2/1)² = 4 : 1

Q3: Check: 30² + 40² = 900 + 1600 = 2500 = 50²

By the Converse of Pythagoras Theorem, Plot X is right-angled at the vertex opposite the 50 m side.

Q4: Area(X)/Area(Y) = 4/1

Area(X) = 4 × 150 = 600 m²

Verify: Area of right-triangle with legs 30 m, 40 m = ½ × 30 × 40 = 600 m²

Theorem summary table

 

Click below to download your free Case Study Questions PDF with worked-out examples for Class 10 Chapter 6: Triangles, perfect for last-minute CBSE exam revision.

Class 10 Chapter 6: Triangles Case Study PDF