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ABCD is a trapezium whose side AD is parallel to BC. Diagonals AC and BD intersect at O. If AO = 3 , CO = x - 3 , BO = 3x - 19 and DO = x - 5 , the value(s) of x will be :
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- 7, 6
- 12, 6
- 7, 10
- 8, 9
- 7, 6
Correct Option: D
As per the given in question , we draw a figure trapezium ABCD
Clearly,
∆AOD ~ ∆BOC
| ∴ | = | ||
| OC | OA |
| ⇒ | = | ||
| x - 3 | 3 |
⇒ 9x – 57 = x2 – 8x + 15
⇒ x2 – 17x + 72 = 0
⇒ x2 – 8x – 9x + 72 = 0
⇒ x (x – 8) – 9 (x – 8) = 0
⇒ (x – 8) (x – 9) = 0
⇒ x = 8 or 9
