The perimeter of a sector of a circle of radius 14 cm is 68 cm. Find the area of the sector.

Options

A. 270 `cm^2`
B. 280 `cm^2`
C. 260 `cm^2`
D. 240 `cm^2`

Answer

B

Explanation

Let O bet the centre of a circle of radius 14 cm.
Let OACBO be the sector whose perimeter is 68 cm.

Then `OA+OB` arc `ACB=68cm`
`implies14cm|14cm arcACB=68cm`
`implies` arc `ACB=(68-28)cm=40cm`
`:.` ar(sector OACBO) `=(1/2xx"radis"xx"arc length")`
`=(1/2xx14xx40)cm^(2)`
`=280cm^(2)`