KVPY SA Exam 2018 Question Paper

Question : 65 of 80

Marks: +1, -0

Suppose ABCD is a trapezium whose sides and height are integers and AB is parallel to CD. If the area of ABCD is 12 and the sides are distinct, then

|AB -CD|

is 2
is 4
is 8
cannot be determined from the data

Validate

Solution:

Given :

1/2(a+b)×h=12

(a+b)×h=24

24 × 1
12 × 2
6 × 4
8 × 3
In height angle.

∆\AED

Possible height for integer sides.
h = 4, 3
Case–I When h = 4
Then possible triplet (3, 4, 5)
i.e. DE = 4, AE = 3, AD = 5
if AE = 3, 2b = 3
b = 3/2
(Not possible because b ∈ I)
Case–II When h = 3
Then AE = 4,
2b = 4
b = 2
∴ CD = 2, AB = 6
∴

| AB -CD| =4

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