ABCD is a trapezium in which AB || DC and its diagonals intersect at P. If AP = (3x – 1) cm, PC = (5x – 3) cm, BP = (2x + 1) cm and PD = (6x – 5) cm, then the length of DB is:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 12 cm
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Concept |
Understanding |
Application |
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Similarity of the triangle |
Given: AB||DC AP = (3x – 1) cm, PC = (5x – 3) cm, BP = (2x + 1) cm and PD = (6x – 5) cm
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Since, AB||DC ∆APB is similar to ∆CPD. Hence, AP/PC = BP/PD (3x – 1)/(5x – 3) = (2x + 1)/(6x – 5) 18x2 - 21x + 5 = 10x2 – x – 3 8x2 - 20x + 8 = 0 2x2 - 5x + 2 = 0 On solving further: 2x2 - 4x – x + 2 = 0 (x – 2) (2x – 1) = 0 Hence, x = 2, 1/2 But x cannot be equal to 1/2 as on putting x = ½, we will get negative values for PD and PC, which is not possible. Putting x = 2 BD = BP + PD = 2x + 1 + 6x – 5 = 12 cm |
