No products in the cart.

Prove that the sum of three …

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Prove that the sum of three altitudes is less than the perimeter of a triangle.

Posted by Kittu Nagar 1 year, 8 months ago

CBSE > Class 09 > Mathematics

1 answers

Shanu Pratap 1 year, 8 months ago

Let ABC be the △ with sides BC,AC and AB opposite to the angles A,B and C being in length equal to a,b and c respectively. To prove:- AL+BM+CN<AB+BC+CA Construction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively. Now, In △ACL, Using pythagoras theorem, AC2=AL2+CL2 ⇒AC2>AL2 ⇒AC>AL.....(1) Similarly, AB>BM.....(2) BC>CN.....(3) Adding equation (1),(2)&(3), we get] AB+BC+AC>AL+BM+CN Hence proved.

ANSWER

http://mycbseguide.com/examin8/

Related Questions

Write the following in decimal form and say what kind of decimal expansion each has 1)36/100

Posted by Koyal Roy 4 days ago

CBSE > Class 09 > Mathematics

2 answers

Simplify √3-²

Posted by Komal Patel 4 days, 19 hours ago

CBSE > Class 09 > Mathematics

0 answers

Factorise x²-54x+350

Posted by Ayan Shukla 1 day, 13 hours ago

CBSE > Class 09 > Mathematics

0 answers

How to draw number line in 360°

Posted by Naman Jain 3 days, 13 hours ago

CBSE > Class 09 > Mathematics

0 answers

x^3+3x^2+3x+1 ÷ 2x+5

Posted by Arnav V Shetty 2 days, 12 hours ago

CBSE > Class 09 > Mathematics

0 answers

The radius of a circle is 3.5meter a car covers 8 rounds of the circle at the speed of 22meter per minute find the taken time

Posted by Aditay Yadav 4 days, 15 hours ago

CBSE > Class 09 > Mathematics

2 answers

(x^a/x^b)^a+b

Posted by Aaradhya Ashish Shastri 2 days, 13 hours ago

CBSE > Class 09 > Mathematics

0 answers

Exercise 1.3 question 6 How to solve this can anyone please tell me ?

Posted by Diya Sarma 3 days, 14 hours ago

CBSE > Class 09 > Mathematics

1 answers

1. A traffic signal board, indicating 'SCHOOL AHEAD', is an equilateral triangle with side "a". Find the area of the signal board, using Heron's formula. If its perimeter is 180 cm, what will be the area of the signal board?

Posted by Anurag Bhardwaj 3 days, 13 hours ago

CBSE > Class 09 > Mathematics

1 answers

Find five rational no 1/3and1/4

Posted by Jashanjot Wadhwa 23 hours ago

CBSE > Class 09 > Mathematics

2 answers

myCBSEguide App

myCBSEguide

Trusted by 1 Crore+ Students

Test Generator

Test Generator

Create papers online. It's FREE.

CUET Mock Tests

CUET Mock Tests

75,000+ questions to practice only on myCBSEguide app

Google Play

Download myCBSEguide App