Question 4 - Case Based Questions (MCQ) - Chapter 6 Class 10 Triangles

Transcript

Question Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1: 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B = 100°, ∠C = 70° and ∠D = 85°. Since the two quadrilaterals are similar Angles will be the same Sides have the ratio as that of scale factor, i.e. 1 : 2 Therefore, ∠A’ = 105°, ∠B’ = 100°, ∠C’ = 70° and ∠D’ = 85° For sides: 𝑨𝑩/(𝑨^′ 𝑩^′ )=𝑩𝑪/(𝑩^′ 𝑪^′ )=𝑪𝑫/(𝑪^′ 𝑫^′ )=𝑨𝑫/(𝑨^′ 𝑫^′ )=𝟏/𝟐 A’B’ = 2 × AB = 2 × 1.5 = 3 cm B’C’ = 2 × BC = 2 × 2.5 = 5 cm C’D’ = 2 × CD = 2 × 2.4 = 4.8 cm A’D’ = 2 × AD = 2 × 2.1 = 4.2 cm Question 1 What is the measurement of angle A’? (a) 105° (b) 100° (c) 70° (d) 80° Here, ∠A' = ∠A ∠ A' = 105° So, the correct answer is (A) Question 2 What is the length of A'B’? (a) 1.5 cm (b) 3 cm (c) 5 cm (d) 2.5 cm Now, A’B’ = 2 × AB = 2 × 1.5 = 3 cm So, the correct answer is (B) Question 3 What is the sum of angles of quadrilateral A'B'C'D’? (a) 180° (b) 360° (c) 270° (d) None of these We know that Sum of angles of any quadrilateral = 360° Sum of angles of A'B'C'D' = 360° So, the correct answer is (B) Question 4 What is the ratio of sides A'B' and A'D’? (a) 5: 7 (b) 7: 5 (c) 1: 1 (d) 1: 2 We found that, A’B’ = 3 cm A’D’ = 4.2 cm Now, ∴ (𝑨^′ 𝑩)/(𝑨^′ 𝑫) = 3/4.2 = 30/42 = 5/7 or 5 : 7 So, the correct answer is (A) Question 5 What is the sum of angles C' and D’? (a) 105° (b) 100° (c) 155° (d) 140° Now, ∴ ∠C' + ∠ D' = 70° + 85° = 155° So, the correct answer is (C)