The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft.^2
Answers
Answer:
length = 4ft
width = 3ft
Step-by-step explanation:
These are the given:
A = lw
l = x + 1ft
w = x
A = 12ft
We'd equate the product of the values of length (l) and width (w) to 12, following the formula of an area. Solution below.
12 = (x+1)(x) substitute and distribute (multiply) x to x + 1
12 = x² + x this should be the result. then transfer the product to the left side of the equal sign.
12 - x² - x = 0 this should be the result. remember that when you transfer a term to the other side of the equal sign, you change the term's sign to its opposite. arrange the terms now.
-x² - x + 12 = 0 this should be the result. the quadratic term (-x²) shall not be negative. thus, we multiply all the terms to -1 to make the quadratic term positive.
x² + x - 12 = 0 this should be the result. factor them.
(x+4) (x-3) = 0 this should be the result. equate each of them to zero now.
x + 4 = 0
x = -4
but since a measurement can't be negative, this value of x is not applicable.
x - 3 = 0
x = 3
we're gonna use this one.
Checking:
12 = lw
12 = (x+1) (x)
12 = (3+1) (3)
12 = (4) (3)
12 = 12
therefore, the value of x is right.