

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Pythagoras Theorem and it's important questions
Question 2 Important Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Deleted for CBSE Board 2024 Exams
Question 6 Deleted for CBSE Board 2024 Exams
Question 4 Important Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 4 Deleted for CBSE Board 2024 Exams
Question 5 Deleted for CBSE Board 2024 Exams
Question 8 Important Deleted for CBSE Board 2024 Exams You are here
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 7 Deleted for CBSE Board 2024 Exams
Question 5 Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 8 Deleted for CBSE Board 2024 Exams You are here
Question 2 (MCQ) Deleted for CBSE Board 2024 Exams
Pythagoras Theorem and it's important questions
Last updated at May 29, 2023 by Teachoo
Question 16 In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes. Given:- Equilateral triangle ABC with each side a & AD as one of its altitudes To Prove :- 3 × Square of one side = 4 × square of one of it’s altitude ⇒ 3a2 = 4AD2 Proof:- In Δ ADB & Δ ADC AB = AC AD = AD ∠ ADB=∠ ADC Hence ∆ ADB ≅ ∆ ADC Hence , BD = DC BD = DC = 1/2BC BD = DC = 𝑎/2 Now, ADB is a right angle triangle Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 (AB)2 = (AD)2 + (BD)2 (a)2 = AD2 + (1/2 𝑎)2 a2 = AD2 + 𝑎2/4 a2 – 𝑎2/4=𝐴𝐷2 (4𝑎2 − 𝑎2)/4=𝐴𝐷2 3𝑎2/4=𝐴𝐷2 3a2 = 4 ×𝐴𝐷2 3a2 = 4AD2 Hence proved