the area of a rectangular plot is 300 square meters. The length of the plot is one more than twice its width. Find the length and width of the plot.

Question

the area of a rectangular plot is 300 square meters. The length of the plot is one more than twice its width. Find the length and width of the plot.

Answer 1

Peyton,

 

 the area of a rectangle is defined as the length times the width. So, let

 

 l: length of rectangle

w: width of rectangle.

 

So, we know that lw=300 (area of rectangle is 300 square meters. I am leaving off the units. In the end, our length and width will both be in meters since meters times meters is square meters.)

 

Also, we know that

 

 l=2w+1  (the length is one more than twice the width). Substituting this value in for l yields

 

(2w+1)w=300 which is the same as

 

2w²+w-300=0   (Distributing and miving everything to one side, since this is a quadratic equation)

 

Using the quadratic formula gives you     w=12 and w=-25/2.   Since a width can't be negative, it must be that w=12. Substituting this value into our equation for length gives us

 

l=2(12)+1=25.  Thus length is 25 meters and width is 12 meters. But is this right? need to check!

 

Does 25*12=300?  Yes it does!     Hope this helps.

 

 

-Sam