Question

in the given figure, the shape of the table top is a sector of circle with Centre O and angle in AOB= 90 degree if AO=OB=42 cm then find the perimeter of the top of the table

Answer 1

In triangle AOB

Angle AOB = 90 deg
and 
AO = OB = 42 Cm
So 
we can say that the triangle is an isosceles Triangle 

Thus 

angle A = Angle B
Thus

2 Angle A = 180 - 90
   Angle A = Angle B = 45 deg
Thus in triangle AOB
Sin 45 = OA/AB
 Thus   AB = 42 root 2
Thus the perimeter of the top of table = AO + OB +AB
                                                            = 84 + 42 root2
                                                            = 42 ( 2 +  root 2)

Answer 2

hope it's helpful to you. . . . .