Question

The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of 6z2 + 6z square meters. Factor this polynomial to find possible expressions for the length and width of the width of the wall

Answer 1

Let A be the area of the wall.

Given that the amount of paint needed to cover a wall paint is proportinal to ts area, and the wall is rectangular with area

$A=6z^2+6z\text{ ---- equation 1}$

Since the wall has a rectangular shape, the area of the wall is evaluated as

$\text{Area of rectangular wall = length}\times width$

From equation 1,

$A=6z^2\text{ + 6z}$

simplify by factorization,

$A\text{ = 6z(z+1)}$

Since the length has a longer dimension than the width, we have

$\begin{gathered} \text{length = 6z} \\ \text{breadth = z+1} \end{gathered}$

Hence, the possible expressions for the length and width of the wall are

$\begin{gathered} \text{length = 6z} \\ \text{width = z+1} \end{gathered}$