Question

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

Answer 1

Answer:

The value of  $x = \frac{1}{6}$

The length of the rectangle   $= \frac{3}{2}$ cm

The width of the rectangle  = $\frac{16}{3}$ cm

Step-by-step 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

             $x = \frac{1}{6}$

The length of the rectangle

                               $= 3 (\frac{1}{6} ) +1 \\= \frac{3}{2}$

The width of the rectangle

                            $= 2 (\frac{1}{6} ) +5$

                            = $\frac{16}{3}$