The areas of two similar triangles ∆ABC and ∆DEF are 144 cm2 and 81 cm2 respectively. If the longest side of larger ∆ABC be 36 cm, then the longest side of the smaller triangle ∆DEF is
The areas of two similar triangles ∆ABC and ∆DEF are 144 cm2 and 81 cm2 respectively. If the longest side of larger ∆ABC be 36 cm, then the longest side of the smaller triangle ∆DEF is
(a) 20 cm
(b) 26 cm
(c) 27 cm
(d) 30 cm
Given: Areas of two similar triangles $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are $144 \mathrm{~cm}^{2}$ and $81 \mathrm{~cm}^{2}$.
If the longest side of larger ΔABC is 36cm
To find: the longest side of the smaller triangle ΔDEF
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
$\frac{\operatorname{ar}(\Delta \mathrm{ABC})}{\operatorname{ar}(\Delta \mathrm{DEF})}=\left(\frac{\text { longest side of larger } \Delta \mathrm{ABC}}{\text { longest side of smaller } \Delta \mathrm{DEF}}\right)^{2}$
$\frac{144}{81}=\left(\frac{36}{\text { longest side of smaller } \triangle \mathrm{DEF}}\right)^{2}$
Taking square root on both sides, we get
129=36longest side of smaller ∆DEF
longest side of smaller $\triangle \mathrm{DEF}=\frac{36 \times 9}{12}=27 \mathrm{~cm}$
Hence the correct answer is C
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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,