$\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}$. If $\mathrm{BC}=3 \mathrm{~cm}, \mathrm{EF}=4 \mathrm{~cm}$ and $\operatorname{ar}(\triangle \mathrm{ABC})=54 \mathrm{~cm}^{2}$, then $\operatorname{ar}(\triangle \mathrm{DEF})=$
(a) $108 \mathrm{~cm}^{2}$
(b) $96 \mathrm{~cm}^{2}$
(c) $48 \mathrm{~cm}^{2}$
(d) $100 \mathrm{~cm}^{2}$
Given: In Δ ABC and Δ DEF
$\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}$
$\operatorname{Ar}(\triangle \mathrm{ABC})=54 \mathrm{~cm}^{2}$
$B C=3 \mathrm{~cm}$ and $E F=4 \mathrm{~cm}$
To find: Ar(Δ DEF)
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
$\frac{\operatorname{Ar}(\Delta \mathrm{ABC})}{\operatorname{Ar}(\Delta \mathrm{DEF})}=\frac{\mathrm{BC}^{2}}{\mathrm{EF}^{2}}$
$\frac{54}{\operatorname{Ar}(\triangle \mathrm{DEF})}=\frac{3^{2}}{4^{2}}$
$\frac{54}{\operatorname{Ar}(\Delta \mathrm{DEF})}=\frac{9}{16}$
$\operatorname{Ar}(\Delta \mathrm{DEF})=\frac{16 \times 54}{9}$
$\operatorname{Ar}(\triangle \mathrm{DEF})=96 \mathrm{~cm}^{2}$
Hence the correct answer is (b)
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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,