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Maths-

General

Easy

Question

In the figure, $stack A B with bar on top divided by divided by stack C D with bar on top$ and $stack A C with rightwards arrow on top intersection stack B D with bar on top equals 0 blank$ 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

Hence AC=12

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Two line segments $stack A B with bar on top$ and $stack C D with bar on top$ intersect at E such that $triangle A C E tilde operator triangle B D E times$ If AE = 4cm, BE = 3cm, CE=6cm and DE = x cm then x = ?

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