Question

prove that in a quadrilateral ABCD,perimeter is greater than twice of any side

Answer 1

yes exampleis l =4cm
                         b=3cm
perimeter=24

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

We know that in a triangle sum of two sides is always greater than the third side.

In ΔABC

AB + BC > AC

⇒ AB + BC + CD > AC + CD ......(1)

In ΔADC

AC + CD > AD ........(2)

From (1) and (2)

⇒ AB + BC + CD > AD

⇒ AB + BC + CD + AD > AD + AD

⇒ Perimeter of quadrilateral ABCD > 2 × AD

Similarly , We can prove that

⇒ Perimeter of quadrilateral ABCD > 2 × AB

⇒ Perimeter of quadrilateral ABCD > 2 × BC

⇒ Perimeter of quadrilateral ABCD > 2 × CD

Hence, The perimeter of the quadrilateral ABCD is greater than twice of any side.