Question

In the adjacent figure SMART , MART is a rhombus with each of its angle as90 in triangle smt = angle smt = 60 degree if Sm = 5 cm find the perimeter of smart

Answer 1

The perimeter of smart is 25cm

Rhombus = MART (Given)

SMT = 5cm (Given)

In ΔSMT,

∠SMT =60° and ∠STM =60°

As sum of all three interior angles of a triangle is 180°, thus in ΔSMT-

∠SMT + ∠STM + ∠MST = 180°

Substituting the values -

60° + 60° + ∠MST = 180° ,

= ∠MST = 60°

Since, ∠ SMT =∠STM  = ∠MST = 60° ,

Therefore, ΔSMT is an equilateral triangle

SM = MT = TS, where SM = 5cm, thus,  

SM = MT = TS = 5cm                                                        

As, MART is a rhombus, thus  -

MA = RT = AR = TM ( All sides of rhombus are equal)

MA = RT = AR = TM  = 5

Therefore,

Perimeter of SMART = MS + AM + RA + TR + ST

= 5+5+5+5+5

= 25 cm  

Answer 2

Answer:

25

Step-by-step explanation:

SMT is an equilateral triangle so all  sides will be equal to 5

then, opp sides of a rhombus are equal so 3 sides will be equal to 5

thus answer- 5+5+5+5+5=25cm