You want to enlarge the size of your rectangular vegetable garden. The area (in square feet) of the enlarged garden is represented by x^2+17x+66.

Question

Write binomials that represent the length and width of the enlarged garden. In the enlarged garden, how many feet longer is the length that the width? The area of the enlarged garden is 266 square feet. Find the dimensions of the original garden and the enlarged garden.

Answer 1

Area = x² + 17x + 66 = (x + 11)(x + 6)

 

One dimension is increased by 11 feet.  The other dimension is increased by 6 feet.

 

 

Now we set the area of the enlarged garden to 266 feet.

 

x² + 17x + 66 = 266

 

 

Subtract 266 to both sides of the equation.

 

x² + 17x - 200 = 0

 

 

Solve for x.   The value of x is the original dimension. 

 

(x - 8)(x + 25) = 0

 

 x = 8      or         x = -25

 

 

But dimensions cannot be negative, so we accept x=8.

 

So your dimensions of the enlarged area is

 

length = 8 + 11 = 19 feet

width = 8 + 6 = 14 feet

 

 

Original garden is 8 feet by 8 feet.