The perimeter (in metres) of a semicircle is numerically equal to its area (in square meters). The length of its diameter is (Take π=
7
22
)
- A11
6
meters - B11
3
meters - C11
2
meters - D11
5
meters
Solution & Step-by-step Explanation
Let the radius of the semicircle be r.
The perimeter of a semicircle is given by πr+2r.
The area of a semicircle is given by
2
1
πr
2
.
According to the problem:
πr+2r=
2
1
πr
2
Since r
=0, we can divide by r:
π+2=
2
1
πr
Substitute π=
7
22
:
7
22
+2=
2
1
×
7
22
×r
7
36
=
7
11
×r
36=11r⟹r=
11
36
meters
The diameter (d) is 2r:
d=2×
11
36
=
11
72
=6
11
6
meters
Option presentation alignment:
11
72
matches option A's original representation structure 6
11
6
.
The perimeter of a semicircle is given by πr+2r.
The area of a semicircle is given by
2
1
πr
2
.
According to the problem:
πr+2r=
2
1
πr
2
Since r
=0, we can divide by r:
π+2=
2
1
πr
Substitute π=
7
22
:
7
22
+2=
2
1
×
7
22
×r
7
36
=
7
11
×r
36=11r⟹r=
11
36
meters
The diameter (d) is 2r:
d=2×
11
36
=
11
72
=6
11
6
meters
Option presentation alignment:
11
72
matches option A's original representation structure 6
11
6
.