Question

The lenght of a rectangle is 12 m more than twice the width.The area of rectangle is 320 square m.Write an equation that can be used to find the lenght and width of rectangle.Also find the dimension of the rectangle

Answer 1

let width be x....
then according to the question length will be 2x+12..
given area =320
area of rectangle=l*b
320=x*(2x+12)
320=2x²+12x
2x²+12x-320=0
by middle term factor ..
2x²+32x-20x-320=0
2x(x+16)-20(x+16)=0
(x+16)(2x-20)=0
x+16=0 , 2x-20=0
x=-16 , x=20/2=10
Length or width cannot be negative.....
So 16 and 10 are the length and width of the rectangle respectively..

Answer 2

Hey there !!!!!

Let width of rectangle=x

According to question length is 12m more than twice of the width

So, length=(2x+12)m

Area of rectangle = 320m²

  x(2x+12)=320

   2x²+12x=320

   x²+6x=160

    x²+6x-160=0
   
    x²+16x-10x-160=0

   x(x+16)-10(x+16)=0

  (x+16)(x-10)=0

  x=-16 or x=10

"x" is the width and it cannot be negative so x=10

When x= 10 

 length =2x+12 =2*10+12= 20+12 =32

So , x²+6x-160=0 is the required equation and
dimensions of rectangle are length =32m width =10m

Hope this helped you.......