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General

Easy

Question

# In the figure, and If OA = 3x – 1, OB = 2x + 1, OC = 5x – 3, OD = 6x – 5 then AC =....units.

- 0
- 12
- 15
- 18

## The correct answer is: 12

### In the question there is a figure and asked to find the value of AC

By solving we can get AC for that first we should find value of x

OA= 3x-1 , OC= 5x-3, OD= 6x-5 , BO = 2x+1
AO/OC = BO/OD
[The diagonals of a Trapezium divide each other proportionally]
(3x-1)/(5x-3) =( 2x+1)/(6x-5)
(3x-1) (6x-5) = (5x-3) ( 2x+1)
3x(6x-5) -1 (6x-5) = 2x(5x-3)+1(5x-3)
18x² -15x -6x +5 = 10x² -6x +5x -3
18x² -21x +5 = 10x² - x -3
18x² -10x² -21x + x +5+3 =0
8x² - 20x +8= 0
4(2x² -5x +2) = 0
2x² -5x +2 = 0
2x² -4x -x +2= 0
[By factorization]
2x(x-2) -1(x-2)= 0
(2x-1) (x-2) = 0
(2x-1) = 0 or (x-2) = 0
x = ½ or x = 2
If we put x= ½ in OD , The value of OD is negative.
Hence, the value of is x = 2.
Since x=2 OA= 3x-1 = 5

OC=5x-3=7

AC = OA+AC=12

OC=5x-3=7

AC = OA+AC=12

Hence AC=12

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