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

Last updated at May 29, 2023 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

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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)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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