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 May 29, 2023 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

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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

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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