Kerala is a state in Southern India. The state is known as a tropical paradise of waving palms and wide sandy beaches.This map the Indian province of Kerala shows its area can be approximated using a
simple straight – sided shape. The shape has two parallel sides 561 km and 216 km long. The other sides are 180 km and 211 km long. Its parallel sides are 100 km apart.
Shreya observed the shape formed by four straight lines and explored it on her notebook in different ways shown below.
Refer to Shape I
a) Let 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 =
i) BF/CD
ii) AB/CD
iii) BF/FC
iv) none of these
b)Here, AB//CD. If DO = 3x−19, OB= x – 5, AO = 3 and OC= x − 3 , then the value of x is
i) 5 or 8 ii) 8 or 9 iii) 10 or 12 iv) none of these
c) Here, AB||CD. If DO = 3x−1, OB= 5x – 3, AO = 6x – 5 and OC= 2x + 1 , then the value of x is
i) 0 ii) 1 iii) 2 iv) 3
Refer to Shape II
d) In ∆ ABC , PQ||BC . If AP=2.4 cm , AQ =2 cm , QC = 3 cm and BC = 6 cm , AB and PQ are respectively
i) AB = 6 cm , PQ = 2.4 cm
ii) AB = 4.8 cm , PQ = 8.2 cm
iii) AB = 4 cm , PQ = 5.3 cm
iv) AB = 8.4 cm , PQ = 2.8 cm
e) In ∆ DEF , if RS||EF , DR = 4x-3 ,DS= 8x – 7, ER = 3x −1 and FS =5x – 3 , then the value of x is
i) 1 ii) 2 iii) 8 iv) 10
Please give explanation
Answers
Step-by-step explanation:
(1.) (iii)
(2.) (i)
(3.) (iii)
(4.) (i)
(5.) (i)
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
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