CBSE Class 10 Maths (Basic) 2024 · Paper 430/3/1 · Question 38

Triangles 4 marks Very hard

In the figure given below, a folding table is shown. The legs of the table are represented by line segments AB and CD intersecting at O. Join AC and BD. Considering table top is parallel to the ground, and

O B = x

O D = x + 3

O C = 3 x + 19

and

O A = 3 x + 4

, answer the following questions :

(i)Prove that $△ O A C$ is similar to $△ O B D$ .
(ii)Prove that $\frac{O A}{A C} = \frac{O B}{B D}$ . (iii)(a) Observe the figure and find the value of $x$ . Hence, find the length of OC. OR (iii)(b) Observe the figure and find $\frac{B D}{A C}$ .

Folding-table legs crossing at O: triangles OAC and OBD

(i)Prove that $△ O A C$ is similar to $△ O B D$ .[1]
(ii)Prove that $\frac{O A}{A C} = \frac{O B}{B D}$ .[1]
(iii)(a)Find the value of $x$ . Hence, find the length of OC.[2]
(iii)(b)Find $\frac{B D}{A C}$ .[2]

Answer

(i)

△ O A C \sim △ O B D

by the AA criterion (alternate angles

∠ O A C = ∠ O B D

and vertically opposite angles

∠ A O C = ∠ B O D

). (ii) Hence

\frac{O A}{A C} = \frac{O B}{B D}

. (iii)(a)

x = 2

, so

O C = 25

. (iii)(b)

\frac{B D}{A C} = \frac{1}{5}

🔒 Step-by-step solution

From the board paper

CBSE Class 10 Maths (Basic) 2024 · Paper 430/3/1, Question 38 — all 38 questions with answers →

CBSE Class 10 Maths (Basic) 2024 · Paper 430/3/1 · Question 38

Answer

From the board paper

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