a wire when bent in the form of an equilateral triangle encloses an area of 49 root 3 cm2, find the largest area enclosed by the same wire when bent to form : (i) a square (ii) a rectangle of length 12 cm.
Dear Student,
Please find below the solution to the asked query:
Given :a wire when bent in the form of an equilateral triangle encloses an area of 49 cm2 ,
We know , Area of equilateral triangle = , So
= 49
Side 2 = 196
Side 2 = 142
Side = 14
Here
Length of wire = Perimeter of given equilateral triangle , So
Length of wire = 14 + 14 + 14 = 42 cm
i ) When that wire bent into a square then length of wire is equal to perimeter of square .
We know perimeter of square = 4 ( Side ) , So
4 ( Side ) = 42
Side = 10.5
And we know area of square = ( Side )2
So,
Area of that square = ( 10.5 ) 2 = 110.25 cm2 ( Ans )
ii ) When that wire bent into a rectangle then length of wire is equal to perimeter of rectangle .
We know perimeter of rectangle = 2 ( Length + Width ) , So
2 ( Length + Width ) = 42
Length + Width = 21 , given length = 12 cm , so
12 + Width = 21
Width = 9 cm
And we know area of rectangle = Length Width
So,
Area of that rectangle = 12 9 = 108 cm2 ( Ans )
Hope this information will clear your doubts about Surface Areas and Volumes .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given :a wire when bent in the form of an equilateral triangle encloses an area of 49 cm2 ,
We know , Area of equilateral triangle = , So
= 49
Side 2 = 196
Side 2 = 142
Side = 14
Here
Length of wire = Perimeter of given equilateral triangle , So
Length of wire = 14 + 14 + 14 = 42 cm
i ) When that wire bent into a square then length of wire is equal to perimeter of square .
We know perimeter of square = 4 ( Side ) , So
4 ( Side ) = 42
Side = 10.5
And we know area of square = ( Side )2
So,
Area of that square = ( 10.5 ) 2 = 110.25 cm2 ( Ans )
ii ) When that wire bent into a rectangle then length of wire is equal to perimeter of rectangle .
We know perimeter of rectangle = 2 ( Length + Width ) , So
2 ( Length + Width ) = 42
Length + Width = 21 , given length = 12 cm , so
12 + Width = 21
Width = 9 cm
And we know area of rectangle = Length Width
So,
Area of that rectangle = 12 9 = 108 cm2 ( Ans )
Hope this information will clear your doubts about Surface Areas and Volumes .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards