Question 34 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

Sides AB and BE of a right triangle, right angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is

(a) 13/100 (b) 13/10 (c) 10/13 (d) 100/13

Ques 34 (MCQ) - Sides AB and BE of a right triangle, right angled at B - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]

part 2 - Question 34 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards - Class 10

part 3 - Question 34 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards - Class 10

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Transcript

Question 34 Sides AB and BE of a right triangle, right angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is (a) 13/100 (b) 13/10 (c) 10/13 (d) 100/13 Let FDGB be a square with side x cm Now, For parallel lines FD and CE with transversal AE ∠ ADF = ∠ AEB Also, since FDGB is a square ∠ AFD = 90° & ∠ DGF = 90° In Δ AFD and Δ DGF ∠ AFD = ∠ DGF ∠ ADF = ∠ AEB ∴ Δ AFD ~ Δ DGF Since sides in similar triangle are proportional 𝐴𝐹/𝐷𝐺=𝐹𝐷/𝐺𝐸 (𝟏𝟔 − 𝒙)/𝒙=𝒙/(𝟖 − 𝒙) (16 − x) (8 − x) = x2 16 (8 − x) − x (8 − x) = x2 128 − 16x − 8x + x2 = x2 128 − 16x − 8x = 0 128 − 24x = 0 128 = 24x 24x = 128 x = 128/24 x = 𝟏𝟔/𝟑 cm So, the correct answer is (b)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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