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Suppose ABCD is a trapezium whose sides ...

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|

A

2

B

4

C

8

D

connot be determined from the data

Text Solution

Verified by Experts

The correct Answer is:
B

Given: `1/2(a+b)xxh=12`
`(a+b)xxh=24`
`24xx1`
`12xx2`
`6xx4`
`8xx3`
In height angle. `DeltaAED` 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 `binI`)
Case-II When h = 3
Then AE = 4, 2b = 4 `=b=4/2=2`
`:.CD=2,AB=6`
`:.|AB-CD|=4`
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