Question:
In figure, Triangle ABC is a right angled triangle at B. Given that AB = 9 cm, AC = 15 cm and D, E are the mid-points of the sides AB and AC respectively, calculate
(i) The length of BC
(ii) The area of ΔADE.
Solution:
In ΔABC, ∠B = 900,
By using Pythagoras theorem
$A C^{2}=A B^{2}+B C^{2}$
$\Rightarrow 15^{2}=9^{2}+B C^{2}$
$\Rightarrow B C=\sqrt{15^{2}-9^{2}}$
$\Rightarrow \mathrm{BC}=\sqrt{225-81}$
$\Rightarrow \mathrm{BC}=\sqrt{144}=12 \mathrm{~cm}$
In ΔABC,
D and E are mid-points of AB and AC
∴ DE ∥ BC, DE = (1/2) BC [By mid−point theorem]
AD = DB = AB/2 = 9/2 = 4.5 cm [∵ D is the mid−point of AB]]
Area of ΔADE = 1/2 ∗AD∗DE
= 1/2 ∗4.5∗6
$=13.5 \mathrm{~cm}^{2}$
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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
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- Atoms
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