A heating duct has a rectangular cross section whose area is 40(inches squared).
If it is 3in longer than it is wide then what is its length and width. i need both equation and answer
Area = Length * Width
If W = x, then L = x+3
40 = x^2 + 3x
x^2 + 3x - 40 = 0
(x+8)(x-5) = 0
For each possible value of x, find x+3.
x cannot be negative, so only one of the two possible number for x is correct.
To find the length and width of the heating duct, we can set up a system of equations based on the given information.
Let's assume the width of the heating duct is 'w' inches. Since the duct is 3 inches longer than its width, the length can be represented as 'w + 3' inches.
The area of a rectangle is calculated by multiplying its length by its width. We are given that the area is 40 square inches, so we can set up the equation:
Length × Width = Area
(w + 3) × w = 40
Now, we can solve this equation to find the values of 'w' (width) and 'w + 3' (length).
Expanding the equation:
w² + 3w = 40
Rearranging the equation to be in standard quadratic form:
w² + 3w - 40 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, let's factorize it:
(w - 5)(w + 8) = 0
Setting each factor equal to zero:
w - 5 = 0 or w + 8 = 0
Solving for 'w':
w = 5 or w = -8
Since the width of a physical object cannot be negative, we discard the solution w = -8. Therefore, the width of the heating duct is 5 inches.
To find the length, we can substitute the width value back into the expression 'w + 3':
Length = 5 + 3 = 8 inches
So, the length of the heating duct is 8 inches, and the width is 5 inches.