How do I do this?

Question

The area of a rectangular wall of a barn is 30 square feet. Its length is 4 feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

The area of a rectangle is length times width.

Let X be the width.

The length is 4 more than twice the width or:  2X + 4

 

So, the area  is (2X+4) times X:   X(2X+4) = 30

 

2X²+4X = 30

2X²+4X-30 = 0  (Now we need to factor the left side of the equation.)

 

(2X + 10)(X - 3) = 0  (At this point there are two possible solutions.  Start with 2X+10=0 as one of the possible solutions.)

 

2X+10=0

2X= -10

X = -5 (This cannot be right because a width of a physical wall cannot be negative number. So we eliminate this possibility.)

 

Try X - 3 = 0.

X = 3  So the width of the wall is 3 ft.

 

The length of the wall is (2)(3) + 4 = 10 ft.