Question

3.

The sides of a rectangle are x cm and (x + 1) cm. A circle has radius of (x + 2) cm. If the
22
sum of the area of the rectangle and the circle is 184 cm². Using n as 22/7find the value of x.

Answer 1

x = 5.00 cm

Explanation:

• area of the rectangle =
`x` x
`(x + 1)`

=
`x^2 + x`

• area of the circle = π r²

=
`(22)/(7)` x
`(x + 2)^2`

=
`(22)/(7)` x
`(x^2 + 4x + 4)`

∴
`x^2 + x` +
`(22)/(7)` x
`(x^2 + 4x + 4) = 184`

⇒
`x^2 + x` +
`(22)/(7) x^2 \space\ + \space\ (88)/(7) x \space\ + \space\ (88)/(7) = 184`

⇒
`(29)/(7)x^2 \space\ + \space\ (95)/(7)x \space\ - (1200)/(7) = 0`

• Using quadratic formula, where

a =
`(29)/(7)`

b =
`(95)/(7)`

c =
`(-1200)/(7)` ,

`x=(-b \pm √(b^2-4c))/(2)`

`x = \frac{-(95)/(7)\pm \sqrt{((95)/(7))^2 - 4((29)/(7))((-1200)/(7) ) } }{2((29)/(7))}`

`x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28`

As length (x) cannot be a negative number,

x = 5.00 cm