in a trapezium ABCD AB|| ab parallel to dc and diagonal AC and BD intersect at point O is equal. toOA 2 X + 7 OB =4 X OD =4 x- 4 OC 2 X + 4 find find the value of x
Answers
Step-by-step explanation:
GIVEN:
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.
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Answer:
GIVEN:-
OA=3X-1 (as we know that in a trapezium diagonals are proportional)
OB=2X+1 OA/OC=OB/OD
OC=5X-3
OD=6X-5
HENCE,
(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.
Hence, the value of is x = 2.
Read more on Brainly.in - https://brainly.in/question/14361449#readmore