Question

The area of this rectangle is 8cm2
(3x + 1) cm
(2x + 5) cm
Work out the value of x

Answer 1

The value of
`x = (1)/(6)`

The length of the rectangle
`= (3)/(2)` cm

The width of the rectangle =
`(16)/(3)` cm

Explanation:

Step(i):-

Given that area of the rectangle = 8 cm²

Length of the rectangle (l) = 3x+1

width of the rectangle (w) = 2x+5

The area of the rectangle = length × width

Given that area of the rectangle = 8 cm²

Step(ii):-

Now

(3x+1) ( 2x+5) = 8

⇒ 3x(2x+5) +1(2x+5) =8

6 x² + 15x + 2x +5 =8

⇒ 6 x² + 17x -3 =0

⇒ 6 x² + 18x -x -3 =0

⇒ 6 x ( x+3) -1(x+3) =0

⇒ 6x -1 =0 and x +3 =0

`6x = 1` and x =-3

`x = (1)/(6)`

The length of the rectangle

`= 3 ((1)/(6) ) +1 \\= (3)/(2)`

The width of the rectangle

`= 2 ((1)/(6) ) +5`

=
`(16)/(3)`