Question

7. In the adjoining figure, ABCD is a trapezium in which CD || AB and its diagonals intersect at 0. If AO = (2x + 1) cm, OC = (5x - 7) cm, DO = (7x-5) cm and OB = (7x +1) cm, find the value of x.


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Answer 1

Answer:

The prime numbers lying between 61 and 75 are, 61, 67, 71 and 73. And sum of these numbers are, 61 +67 +71+73 = 272.

Answer 2

Answer:

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From given statement:

In △ADC

EO∣∣AB∣∣DC

By thales theorem:

ED

AE

=

OC

AO

...(1)

In △DAB

EO∣∣AB

So, By thales theorem:

EA

DE

=

OB

DO

...(2)

From (1) and (2)

OC

AO

=

OB

DO

(2x+1)

(5x−7)

=

(7x+1)

(7x−5)

(5x−7)(7x+1)=(7x−5)(2x+1)

35x

2

+5x–49x–7=14x

2

–10x+7x−5

35x

2

−14x

2

–44x+3x−7+5=0

21x

2

−42x+x−2=0

21(x−2)+(x−2)=0

(21x+1)(x−2)=0

Either (21x+1)=0 or (x–2)=0

x=

21

−1

(does not satisfy) or x=2

⇒x=2.