Question 34 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards
Last updated at Sept. 6, 2021 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)
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
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