Answer:
Width = x-6 metres
Step-by-step explanation:
The formula for the area of a rectangle is represented by Length (l) × Width (w).
If the area is x^2-4x -12, which is an algebraic expression, The best way to find its length and breadth which would be a product of themselves is by FACTORIZATION.
To factorize x^2-4x -12, we say:
×^2 = a, -4x = b, -12 = c
Product: a×c; -12 × x^2= -12x^2
Sum: b; -4x derived by saying (-6x+2x)
Note that the expression of the sum (-6x+2x) must be able to be multiplied to give product (-12x^2).
Hence, we rewrite our algebraic expression using the sum expression.
x2 - 6x + 2x - 12
We then factorize by using a common factor (x and 2)
x( x - 6) + 2 (x - 6)
(x+2) (x-6)
Thus, the factors are x+2 and x-6
This means that (x+2) and (x-6) will be multiplied to give x^2-4x-12. Therefore, if x+2 metres is the Length, x-6 metres is the width.
