In the given figure, $\triangle \mathrm{ACB} \sim \triangle \mathrm{APQ}$. If $\mathrm{BC}=10 \mathrm{~cm}, \mathrm{PQ}=5 \mathrm{~cm}, \mathrm{BA}=6.5 \mathrm{~cm}$ and $\mathrm{AP}=2.8 \mathrm{~cm}$, find $\mathrm{CA}$ and $\mathrm{AQ}$. Also, find the area $(\triangle \mathrm{ACB}):$ area $(\triangle \mathrm{APQ})$.
Given: ΔACB is similar to ΔAPQ.
BC = 10 cm, PQ = 5cm, BA = 6.5cm and AP = 2.8 cm
TO FIND:
(1) CA and AQ
(2) Area of ΔACB : Area of ΔAPQ
(1) It is given that ΔACB ~ ΔAPQ.
We know that for any two similar triangles the sides are proportional. Hence
ABAQ=BCPQ=ACAP
$\frac{\mathrm{AB}}{\mathrm{AQ}}=\frac{\mathrm{BC}}{\mathrm{PQ}}$
$\frac{6.5}{\mathrm{AQ}}=\frac{10}{5}$
$\mathrm{AQ}=3.25 \mathrm{~cm}$
Similarly,
$\frac{\mathrm{BC}}{\mathrm{PQ}}=\frac{\mathrm{CA}}{\mathrm{AP}}$
$\frac{\mathrm{CA}}{2.8}=\frac{10}{5}$
$\mathrm{CA}=5.6 \mathrm{~cm}$
(2) We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar∆ACQar∆APQ=BCPQ2=1052=212=41
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- 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,