Question

In the given figure,if LK=6√3 find MK,LK,KN,MN and the perimeter of quadrilateral MNKL.

Answer 1

Given: LK = 6√3

To find: The value of  MK, LK, KN, MN and the perimeter of quadrilateral MNKL.

Solution:

• Now we have given LK = 6√3.

• Now consider the triangle LKM, we get:

                   tan 30 = ML/LK

                   ML = √3 x 1/√3 = 1

                   cos 30 = LK/MK

                   MK = √3/√3/2 = 2

• Now from the figure, we get:

                   MK = NK = 2..................(side opposite to equal angle)

• In triangle MKN, we have:

                   sin 45 = NK/MN

                   NK = 2√2

• Now perimeter of the quadrilateral is:

                   2√2 + 2 + √3 + 1 = ( 2√2 + 3 + √3 ) units

Answer:

               So the sides of the quadrilateral are 2√2 units, 2 units, √3 units, 1 unit and perimeter is  ( 2√2 + 3 + √3 ) units.

Answer 2

Answer:

Mk = 12, Ml = 6 ,kn = 12 , mn = 12 √2 perimeter of quadrilateral MNKL 6(3+2√2 + √3)

hope it will help you....