(i) In the given figure, if AB || CD, find the value of x.
(ii) In the given figure, If AB || CD, find the value of x.
(iii) In the given figure, AB || CD, If OA = 3x − 19, OB = x − 4, OC = x − 3 and OD = 4, find x.
(i) It is given that $A B \| C D$.
We have to find the value of $x$.
Diagonals of the para
Now $\frac{D O}{O A}=\frac{C O}{O B}$
$\Rightarrow \frac{4 x-2}{4}=\frac{2 x+4}{x+1}$
$4(2 x+4)=(4 x-2)(x+1)$
$8 x+16=x(4 x-2)+1(4 x-2)$
$8 x+16=4 x^{2}-2 x+4 x-2$
$-4 x^{2}+8 x+16+2-2 x=0$
$-4 x^{2}+6 x+18=0$
$4 x^{2}-6 x-18=0$
$4 x^{2}-12 x+6 x-18=0$
So
$4 x(x-3)+6(x-3)=0$
$(4 x+6)(x-3)=0$
Therefore $4 x+6=0$ and $x-3=0$
Hence $x=3$
(ii) It is given that $A B \| C D$
We have to find the value of $x$
Now $\frac{D O}{O A}=\frac{C O}{O B}$
$\Rightarrow \frac{6 x-5}{2 x+1}=\frac{5 x-3}{3 x-1}$
$(6 x-5)(3 x-1)=(2 x+1)(5 x-3)$
$3 x(6 x-5)-1(6 x-5)=2 x(5 x-3)+1(5 x-3)$
$18 x^{2}-15 x-6 x+5=10 x^{2}-6 x+5 x-3$
$18 x^{2}-10 x^{2}-21 x+5+x+3=0$
$8 x^{2}-20 x+8=0$
$8 x^{2}-16 x-4 x+8=0$
$8 x(x-2)-4(x-2)=0$
$(8 x-4)(x-2)=0$
So
$(8 x-4)(x-2)=0$
Therefore $8 x-4=0$ or $x-2=0$
Hence x = 12 or x = 2.
For $x=12, \mathrm{OD}$ is negative.
Hence $x=2$
(iii) It is given that $A B \| C D$.
And $O A=3 x-19, O B=x-4 O C=x-3$ and $O D=4$
We have to find the value of $x$
Now $\frac{A O}{O C}=\frac{B O}{O D}$
$\Rightarrow \frac{3 x-19}{x-3}=\frac{x-4}{4}$
$4(3 x-19)=(x-3)(x-4)$
$12 x-76=x(x-4)-3(x-4)$
$12 x-76=x^{2}-4 x-3 x+12$
$12 x-76=x^{2}-7 x+12$
$-x^{2}+7 x-12+12 x-76=0$
$-x^{2}+19 x-88=0$
$x^{2}-19 x+88=0$
So
$x^{2}-11 x-8 x+88=0$
$x(x-11)-8(x-11)=0$
Therefore $x-11=0$ and $x-8=0$
Hence $x=8$ or $x=11$.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,