Question

If LK =6(3) find MK ML KN MN find perimeter of MNKL

Answer 1

Answer:

MK = 12units ,ML= 6units ,NK = 12 units, MN= 12√2 units, perimeter = 6(√3+3+2√2) units

Step-by-step explanation:

In triangle MLK,

tan K = ML/KL

tan 30° = ML/ (6√3)

(1/√3) = ML/ (6√3)

ML = 6√3/√3

ML = 6 units

According to Pythagoras theorem,

MK = √( ML²+ KL²)

= √ [(6)²+(6√3)²]

= √(36+108)

= √ 144 = 12 units

In triangle MKN,

sin N = MK/MN

sin 45° = 12/MN

1/√2 = 12/MN

MN = 12√2 units

Here, MK = KN (sides opp. to equal angles are equal)

MK = KN = 12 units

Perimeter of MNKL = MN+KN+ML+KL

= 12√2+12+6+6√3

= 6(2√2+2+1+√3)

= 6(2√3+3+√3) units