In a country, one of its states is known as tropical paradise of waving palms and wide sandy
beaches. Its map shows that its area can be approximated using simple straight sided shape.
The shape has two parallel sides 561 km. and 261km. long. The other two sides are 180 km
and 211 km. long. Its parallel sides are 100 km. apart. Raghav observed the shape formed by
four straight lines and explored it in his notebook in different ways shown below:-
D
DE
Shape 1
Shape 2
Answers
Given : ABCD is a trapezium with AB||DC , E and F are points on non–parallel sides AD and BC respectively such that EF||AB.
To Find : AE/ED =
i) BF/CD
ii) AB/CD
iii) BF/FC
iv) none of these
Solution:
ABCD is a trapezium with AB||DC , E and F are points on non–parallel sides AD and BC respectively such that EF||AB. Then
AE/ED = BF/FC
ΔDOC ≈ ΔBOA ( using alternate angle and vertical opposite angles )
=> DO/BO = CO/AO
=> (3x-19)/(x-5) = (x - 3)/3
=> 9x - 57 = x² - 8x + 15
=> x² - 17x + 72 = 0
=> (x - 8)(x - 9) = 0
=> x = 8 or 9
8 or 9
DO/BO = CO/AO
=> (3x-1)/(5x-3) = (2x + 1)/(6x - 5)
=> 18x² - 21x + 5 = 10x² -x - 3
=> 8x² - 20x + 8 = 0
=> 2x² - 5x + 2 = 0
=> 2x² - 4x - x + 2 = 0
=> 2x(x - 2) - 1(x - 2) = 0
=> x = 1/2 or x = 2
x = 1/2 not possible as 6x - 5 , 5x - 3 will be -ve then
hence x = 2
Learn More:
There is a trapezium whose parallel sides are 10 cm and 22.3 CM ...
https://brainly.in/question/6716688
JKLM is a trapezium where JK II ML. If the diagonals MK and JL ...
https://brainly.in/question/21236908
