The areas of two similar triangles are $169 \mathrm{~cm}^{2}$ and $121 \mathrm{~cm}^{2}$ respectively. If the longest side of the larger triangle is $26 \mathrm{~cm}$, find the longest side of the smaller triangle.
Given: The area of two similar triangles is $169 \mathrm{~cm}^{2}$ and $121 \mathrm{~cm}^{2}$ respectively. The longest side of the larger triangle is $26 \mathrm{~cm}$.
To find: Longest side of the smaller triangle
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
$\frac{a r(\text { larger triangle })}{a r(\text { smaller triangle })}=\left(\frac{\text { side of the larger triangle }}{\text { side of the smaller triangle }}\right)^{2}$
$\frac{169}{121}=\left(\frac{\text { side of the larger triangle }}{\text { side of the smaller triangle }}\right)^{2}$
Taking square root on both sides, we get
$\frac{13}{11}=\frac{\text { side of the larger triangle }}{\text { side of the smaller triangle }}$
$\frac{13}{11}=\frac{26}{\text { side of the smaller triangle }}$
side of the smaller triangle $=\frac{11 \times 26}{13}=22 \mathrm{~cm}$
Hence, the longest side of the smaller triangle is $22 \mathrm{~cm}$.
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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,