Question

A solar panel has an area of x2 + 21x + 108. Find the possible dimensions of the solar panel.

Answer 1

Answer:

(x + 9) and (x + 12) are possible dimensions of the solar panel

Step-by-step explanation:

Given:

`The\text{ area of the solar panel is }x^2\text{ + 21x + 108}`

To find:

The possible dimensions of the solar panel

To determine the possible dimensions, we will factorise the quadratic function:

`\begin{gathered} x^2\text{ + 21x + 108} \\ factors\text{ of 108 whose sum gives 21: 12 and 9} \\ x^2+\text{ 21x + 108 = x}^2\text{ + 12x + 9x + 108} \end{gathered}`
`\begin{gathered} x^2\text{ + 12x + 9x + 108 } \\ x(x\text{ + 12\rparen + 9\lparen x + 12\rparen } \\ (x\text{ + 9\rparen\lparen x + 12\rparen } \\ \\ x^2\text{ + 21x + 108 = \lparen x + 9\rparen \lparen x + 12\rparen} \end{gathered}`

(x + 9) and (x + 12) are possible dimensions of the solar panel