Question

The length of the rectangle is 3ft less than twice the width,and the area of the rectangle is 27ft^2,find the diameter

Answer 1

Answer:

The dimensions of rectangle are:

• width = w = 4.5 ft

• length = l = 6 ft

Step-by-step explanation:

Let 'l' be the length and 'w' be the width of the rectangle

• The length 'l' of the rectangle is 3ft less than twice the width 'w'.

so

$l=2w-3$

Also, the area of the rectangle is 27ft^2.

$A=27\:ft^2$

As the area of the rectangle has the formula:

$\:A\:=\:l\times w$

so

$27=\:l\times w$

so the equation becomes

$27=\left(2w-3\right)\times \:w$

$27=2w^2-3w$

$2w^2-3w-27=0$

$\left(w+3\right)\left(2w-9\right)=0$

if   $ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$w+3=0\quad \mathrm{or}\quad \:2w-9=0$

$w=-3,\:w=\frac{9}{2}$

as the width can not be negative, so

$w=\frac{9}{2}=4.5$ ft

As

$l=2w-3$

$l=2\left(4.5\right)-3$

$l=9-3$

$l=6$

So the dimensions of rectangle are:

• width = w = 4.5 ft

• length = l = 6 ft