Question

9. A rectangle has a length that is 2 less than 3 times the width. If the
area of this rectangle is 16. find the dimens ons and the perimeter.​

Answer 1

Answer:

Let width be x.

Length be ( 3x - 2)

Area = 16 cm²

x( 3x - 2) = 16

=> 3x² - 2x - 16 =0

=> 3x² - 6x +8x - 16 =0

=> 3x ( x - 2) + 8 ( x - 2) =0

=> ( 3x + 8) ( x - 2) =0

=> x = 2

So,

Width = 2cm

Length = 4 cm

HOPE THIS HELPS YOU! :)

Answer 2

Answer:

Width = $\frac{8}{3}$ units,

Length = $6$ units   and

Perimeter = $\frac{52}{3}$ units or 17.33 units

Step-by-step explanation:

here, Let the width be $x$

length = $3x-2$

Area = 16 units

now, Area = L× B

           16 = $3x-2$ × $x$

           16 = $3x^{2}-2x$

so,  $3x^{2}-2x-16=0$

⇒ $3x^{2}+6x-8x-16=0$

⇒ $3x(x+2)-8(x+2)=0$

⇒ $(x+2)(3x-8)=0$

so, $x+2=0$  = $x=-2$

$3x-8=0$   = $x = \frac{8}{3}$

Width = $\frac{8}{3}$ units

Length = $\frac{8}{3}*3-2$  = $6$ units

Perimeter = 2(l+b)

                = 2($\frac{8}{3}$ + $6$)

                = $2*\frac{26}{3}$

                = $\frac{52}{3}$ units or 17.33 units

hope it will help you.