Question #94454

1 Answer
Nov 8, 2017

#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#