Question

prove that the sum of altitude of triangle is less than the sum of three sides ​

Answer 1

Answer:

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,

AC

2

=AL

2

+CL

2

⇒AC

2

>AL

2

⇒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 2

Answer

AnswerLet 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.

AnswerLet 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

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2 ⇒AC>AL.....(1)

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2 ⇒AC>AL.....(1)Similarly,

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2 ⇒AC>AL.....(1)Similarly,AB>BM.....(2)

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2 ⇒AC>AL.....(1)Similarly,AB>BM.....(2)BC>CN.....(3)

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2 ⇒AC>AL.....(1)Similarly,AB>BM.....(2)BC>CN.....(3)Adding equation (1),(2)&(3), we get]

AnswerLet 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+CAConstruction:- Draw perpendiculars AL,BM and CN from A,B and C to opposite sides meeting respectively.Now,In △ACL,Using pythagoras theorem,AC 2 =AL 2+CL 2⇒AC 2>AL 2 ⇒AC>AL.....(1)Similarly,AB>BM.....(2)BC>CN.....(3)Adding equation (1),(2)&(3), we get]AB+BC+AC>AL+BM+CN