Question

The rectangle below has an area of x^2-4x-12x 2 −4x−12x, squared, minus, 4, x, minus, 12 square meters and a length of x+2x+2x, plus, 2 meters. What expression represents the width of the rectangle?

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation:

Given:

Area of a rectangle = x^2 - 4x - 12 m^2

Length, L = x + 2 m

Area of a rectangle = length × width, B

x^2 - 4x - 12 = (x + 2) × B

B = (x^2 - 4x - 12)/(x + 2) ( by long division)

= x - 6 m