Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

Triangle ABC is right angled at B and D is mid point of BC. Prove that : AC2 = 4AD2 - 3AB2.
Asked by Topperlearning User | 26 Jul, 2017, 02:00: PM
answered-by-expert Expert Answer

In right ABC, using Pythagoras theorem, we have:

AC2 = AB2 + BC2 ...(1)

In right ABD, using Pythagoras theorem, we have:

AD2 = AB2 + BD2

BC2 = 4AD2 - 4AB2 ...(2)

Substituting (2) in (1), we get,

AC2 = 4AD2 - 3AB2

Hence, proved.

Answered by | 26 Jul, 2017, 04:00: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
equilateral triangle ABC , D is a point on side BC such that 3BD = BC. Prove that 9AD2 = 7AB2.
question image
Asked by deepak13376 | 23 Sep, 2020, 01:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Question
question image
Asked by arindeep.singh | 27 Apr, 2020, 10:26: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
If A is the area of right triangle and b is one of the sides containing the right angle,then prove that the length of the altitude on the hypotenuse is 2Ab/√(b^4+4A^2)
Asked by rhtwatts | 06 Mar, 2019, 03:59: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
The height of a moving truck is 8 m. The distance from the bottom edge of the ramp on the ground to the truck is 15 m. What is the length of the ramp?
Asked by Topperlearning User | 26 Jul, 2017, 01:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
In an equilateral triangle AD is the altitude drawn from A on side BC. Prove that 3AB2 =4AD2
Asked by Topperlearning User | 26 Jul, 2017, 01:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
The area of a right triangle is 210 sq cm. If the smallest side is 12 cm, what is the hypotenuse?
Asked by Topperlearning User | 26 Jul, 2017, 01:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
What is the value of a if a, a-1,a+8 are the lengths of the sides of a right triangle where a is a natural number?
Asked by Topperlearning User | 26 Jul, 2017, 01:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
In quadrilateral ABCD, angle B space equals space 90 degree. If AD2 = AB2 + BC2 + CD2. Prove that angle A C D space equals space 90 degree.
Asked by Topperlearning User | 26 Jul, 2017, 01:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
The diagonals AC and BD of a rhombus ABCD are of length 6 cm and 8 cm respectively. What is the perimeter of the rhombus?
Asked by Topperlearning User | 05 Dec, 2013, 08:56: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Prove that if for a right triangle the sides containing the right angle have even numbers as their lengths, then the third side can"t be an odd number.
Asked by Topperlearning User | 26 Jul, 2017, 01:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×