CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

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

Last updated at Nov. 1, 2019 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

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

CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.