Question

The equation represents the area, A, of a rectangle, in square units.

A = x2 – 3 – 6
Which expression could represent the length of the rectangle, in units?
O (2-3)
O (2-2)
Ox
O 6.2

Answer 1

An expression that could represent the length of the rectangle, in units is: A. (x-3)

In Mathematics and Euclidean Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = lw

Where:

• A represent the area of a rectangle.
• w represent the width of a rectangle.
• l represent the length of a rectangle.

By using the factorization method, we would factorize the quadratic equation representing the area of this rectangle as follows;

`A=x^2-x-6\\\\0=x^2-x-6\\\\0=x^(2) -3x+2x-6\\\\0=x(x-3)+2(x-3)\\\\`

0 = x(x - 3) + 2(x - 3)

0 = (x + 2)(x - 3)

x = 3 units since the dimension cannot be negative.

Complete Question:

The equation represents the area, A , of a rectangle, in square units.

`A=x^2-x-6`

Which expression could represent the length of the rectangle, in units?

(x-3)

(x-2)

x

6x

Answer 2

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