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.

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