Question

A rectangular vegetable garden will have a width that is 4 feet less than the length and an area of 140 square feet if x represents the length then the length can be found by solving the equation:
If x represents the length, then the length can be found by solving the equation: x(x-4)=140

Answer 1

Answer: x(x-4) = 140 This equation can be solve to find the length.

Step-by-step explanation:

If the width of the rectangle will be 4 less than the length and the length is represented by x then we could have the equation   w=x - 4 for the width and the length is just x. And to find the area of a rectangle we multiply the length by the with so multiply x-4 by x  for it to equal 140 because 140 is the area.

x(x-4) = 140   solve for x

$x^{2}$ - 4x = 140   subtract 140 from both sides  

x^2 - 4x - 140 = 0  find a number that the product is 140 and the sum is -4

                                  -14 and 10 works out.

$x^{2}$ - 14x + 10x - 140 = 0  factor by grouping

x(x -14)  10(x-14) = 0     factor out x-14

(x-14) ( x+10) = 0         set them both equal zero.

x-14= 0      or   x+10 = 0

x = 14      or x= -10  

Since -10 can't represent a distance, the answer is 14.

Check.  

In this case the length is 14  and if the width is 4 less than the length then we will subtract 4 from 14.

14- 4 = 10  so the width is 10.

14 * 10 = 140