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Question 29 (OR 1st question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

In the figure, ABCDE is a pentagon with BE ∥ CD and BC ∥ DE. BC is perpendicular to CD. AB = 5cm, AE = 5cm, BE = 7cm, BC =  x − y and CD =  x + y. If the perimeter of ABCDE is 27 cm. find the value of x and y, given x, y ≠ 0

Transcript

Question 29 (OR 1st question) In the figure, ABCDE is a pentagon with BE ∥ CD and BC ∥ DE. BC is perpendicular to CD. AB = 5cm, AE = 5cm, BE = 7cm, BC = x − y and CD = x + y. If the perimeter of ABCDE is 27 cm. find the value of x and y, given x, y ≠ 0 Since BE ∥ CD and BC ∥ DE, and BC is perpendicular to CD That means that BCDE is a rectangle And, in a rectangle Opposite sides are equal BE = CD 7 = x + y x + y = 7 Now, Given Perimeter of Pentagon = 27 cm AB + AE + BC + ED + CD = 27 5 + 5 + (x – y) + (x + y) + (x – y) = 27 10 + 3x – y = 27 3x – y = 27 – 10 3x – y = 17 Now, our equations are x + y = 7 …(1) 3x – y = 17 …(2) Adding (1) and (2) (x + y) + (3x – y) = 7 + 17 4x = 24 x = 24/4 x = 6 Putting x = 6 in (1) x + y = 7 6 + y = 7 y = 7 – 6 y = 1 So, x = 6, y = 1 is the solution
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Davneet Singh

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