Triangles — Class 10 Maths MCQ with Answers (2026-27)

Updated 23 August 2026 · checked against the CBSE 2026-27 syllabus

12 objective questions on Triangles, every one checked against the CBSE 2026-27 syllabus. Pick an option and the correct answer is shown straight away, with your marks running at the top. A new question opens each day until all 12 are unlocked.

Triangles MCQ questions with answers

1. Vijay is trying to find the height of a tower using similar triangles. Vijay's house is 20​ m‌ high and casts a shadow 10 m long. At the same time, the tower casts a shadow 50 m long and Ajay's house casts a 20 m shadow. What is the height of the tower?
   1. 20 m
   2. 50 m
   3. 100 m
   4. 200 m

   Answer: c) 100 m

   The sun's rays make equal angles, so the triangles are similar and height ÷ shadow is constant. Vijay's ratio is 20/10 = 2, so the tower is 2 × 50 = 100 m.

2. What will be the length of the shadow of the tower when Vijay's house‌ casts‌ a shadow of 12 m?
   1. 75 m
   2. 50 m
   3. 45 m
   4. 60 m

   Answer: d) 60 m

   Corresponding sides are proportional: tower shadow = 100 × (12/20) = 60 m.

3. What is the height​ of​ Ajay's house?
   1. 30 m
   2. 40 m
   3. 50 m
   4. 20 m

   Answer: b) 40 m

   Using the same ratio of 2, Ajay's house is 2 × 20 = 40 m high.

4. When the tower casts a shadow of 40 m, what will be the length of the shadow of Ajay's house‌ at​ the same time?
   1. 16 m
   2. 32 m
   3. 20 m
   4. 8 m

   Answer: a) 16 m

   The tower's height-to-shadow ratio is 100/40 = 2.5, and it is the same for every object at that moment. Ajay's house: 40 ÷ 2.5 = 16 m.

5. When the tower casts a shadow of 40 m, what will be the length of the shadow of Vijay's house at​ the‌ same time?
   1. 15 m
   2. 32 m
   3. 16 m
   4. 8 m

   Answer: d) 8 m

   Using the same ratio of 2.5, Vijay's house casts 20 ÷ 2.5 = 8 m.

6. A scale drawing of an object is the same shape as the object but a different size; the ratio of two corresponding sides in similar figures is the scale factor. In a photograph of a train engine the scale factor is 1:200. If the length of the model is 11 cm, then the overall length of the‌ engine‌ is
   1. 22 cm
   2. 220 cm
   3. 220 m
   4. 22 m

   Answer: d) 22 m

   Scale 1:200 means every 1 cm on the photograph is 200 cm in reality. So 11 × 200 = 2200 cm = 22 m.

7. What is the​ actual​ width of the door if the width of the door in the photograph is 0.35 cm?
   1. 0.7 m
   2. 0.7 cm
   3. 0.07 cm
   4. 0.07 m

   Answer: a) 0.7 m

   0.35 × 200 = 70 cm, which is 0.7 m. Watch the unit conversion — this is where most marks are lost.

8. Refer to the figure in your textbook or question paper.

   *(Figure required: A at top; AB = x cm along AD; B on AD with BD = 4 cm; BC = 3 cm; DE‌ =​ 6 cm; BC ∥ DE.)* The length of AB in the given figure is
   1. 8 cm
   2. 6 cm
   3. 4 cm
   4. 10 cm

   Answer: c) 4 cm

   BC ∥ DE makes △ABC ~ △ADE, so AB/AD = BC/DE. That gives x/(x + 4) = 3/6, so 2x = x + 4 and x = 4 cm.

9. Refer to the figure in your textbook or question paper.

   *(Figure required: QR ∥ ST, with P, S, Q collinear.)* QR = a, QS = b, SP = c and ST =​ x.​ The correct relationship between x, a, b and c is
   1. x = a(b+c)/c
   2. x = a(b+c)/b
   3. x = ac/(b+c)
   4. x = a(b−c)/b

   Answer: c) x = ac/(b+c)

   ST ∥ QR makes △PST ~ △PQR, so ST/QR = PS/PQ. Since PQ = b + c, x/a = c/(b + c), giving x = ac/(b + c).

10. A water tower for a locality is 40 m high. The water tower casts a shadow‌ of​ 25 m. At the same time, a tree near it casts a shadow of 5 m. What is the height of the tree?
    1. 3.12 m
    2. 8 m
    3. 20 m
    4. 25 m

    Answer: b) 8 m

    At the same moment the height-to-shadow ratio is the same for both: 40/25 = h/5, so h = 8 m.

11. A scale model of the water tower of 100 cm height is created. The height of its​ pillars‌ is 75 cm each. What is the height of a pillar (in m) in the actual water tower?
    1. 7.5
    2. 25
    3. 30
    4. 53.4

    Answer: c) 30

    The model is 100 cm = 1 m tall for a real tower of 40 m, a scale factor of 40. So the pillar is 0.75 × 40 = 30 m.

12. Refer to the figure in your textbook or question paper.

    *(Figure required: a dollhouse roof; triangles‌ ABC‌ equilateral with side 45 cm; DE and GF parallel to the floor divide AB and AC into three equal parts.)* Which criterion of similar triangles does not apply to triangles AGF and ADE?
    1. AAA
    2. SSS
    3. SAS
    4. RHS

    Answer: d) RHS

    AAA, SSS and SAS are all criteria for similarity. RHS is a congruence criterion for right triangles, so it does not apply here.