Answer:
Length of the arc of this sector, l = 14 cm
Explanation:
It is given that, the perimeter of a sector of a circle is the sum of the two sides formed by the radii and the length of the included arc.
Perimeter of sector, P = 28 cm
Area of sector, [tex]A=49\ cm^2[/tex]
According to figure,
2r + l = 28 ............(1)
Area of sector, [tex]A=\dfrac{\theta}{360}\times \pi r^2[/tex]
Where, [tex]\theta[/tex] is in radian and [tex]\theta=\dfrac{l}{r}[/tex]
Since, [tex]1^{\circ}=\dfrac{\pi}{180}\ radian[/tex]
[tex]A=\dfrac{l}{2\pi r}\times \pi r^2[/tex]
[tex]r=\dfrac{98}{l}[/tex]
Put the value of r in equation (1) so,
[tex]2\times (\dfrac{98}{l})+l=28[/tex]
[tex]l^2-28l+196=0[/tex]
On solving above equation for l we get, l = 14 cm. So, the length of the arc of this sector is 14 cm. Hence, this is the required solution.
