Question

Question #94454

Answer 1

`therefore` length`= 25 ft.` and width `= 12 ft.`

Explanation:

Let the width of the rectangle be `w` ft.
So, according to given data:

length `l = 1ft.+ 2w`

Area of rectangle `A = l xx w= 300 ft.^2`

`therefore` 300 Ft^2 = w xx l #

`=> w xx (2w+1) = 300`

`=> 2w^2 + w =300`

`=> 2w^2 + w -300 =0`

Solve this quadratic equation:

We need two such numbers which add upto to give coefficient of middle term (+1) and whose product is equal to the product of coefficient of first term and last term( 2 x 300 =600).

Two such numbers are `25 and -24`

`=> 2w^2 -24w + 25w - 300 =0`

`=> 2w(w - 12) + 25( w - 12) =0`

`=. (2w +25) (w-12)= 0`

`therefore (2w+25)=0 or (w-12)=0`

`=> 2w =-25 => w= -25/2 = -12.5`

But width cannot be negative. So, we take the other value,

`=> w=12`

So, the dimensions are :

`w=12`ft.
and
`l= 1 + 2w = 1+24 = 25`

`therefore`le`n`gth`= 25 and width = 12`