Question
In the figure
OB = 2x + 1, OC = 5x – 3, OD = 6x – 5 then AC = ? units.
- 0
- 12
- 15
- 18
Hint:
find the similar triangles and make the side ratios same and solve for x.
The correct answer is: 12
12
Given, CD || AB. This implies that triangles OCD and OAB are similar by angle angle angle axiom of similarity.
(alternate angles)
Here, < ODC = < OBA
< OAB = <OCD
Therefore, we can use the property that ratio of sides remains same in similar triangles.
OA/OC= OB/OD
=> 3x-1/5x-3 = 2x+1/6x-5
=> (3x-1)(6x-5)=(2x+1)(5x-3)
=> 18x2-21x +5 = 10x2 -x-3
On solving we get
2x2 -5x +2 =0
2x2 - 4x - x + 2 = 0
2x(x-2) -1(x-2) = 0
(2x-1)(x-2) = 0
either 2x -1 = 0 => x=0.5
or x-2 = 0 => x= 2
X= 0.5,2
AC = OA+ OC = 3x+1 + 5x -3 = 8x – 4
On substituting the values of x, we get
AC = 0, 12
Since AC can’t be 0, 12 Is the required answer.
solving the quadratic equations by the factorization method is used. in this method, the linear term is broken down into 2 terms so that we can take out the common factors from the terms and convert the equation into product form.
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