A square photograph is printed on a larger rectangular sheet of paper leaving a border around the
photograph of 2 centimeters on the top and 3 centimeters on each of the remaining sides. The sheet of paper
has an area of 72 square centimeters. If x is the length of a side of the photograph measured in centimeters,
which of the following equations could be used to find x ?

The area of a shape is the amount of space, the shape can occupy. The equation to calculate the value of x is: [tex](e)\ x^2 + 11x -42= 0[/tex]

The space on the border is given as:

[tex]Top = 2[/tex]

[tex]Others = 3[/tex]

So, the dimension of the sheet of paper is:

[tex]Length = x + 2 + 3[/tex]

[tex]Length = x + 5[/tex]

[tex]Width = x + 3 + 3[/tex]

[tex]Width = x + 6[/tex]

The area of the sheet is then calculated as follows:

[tex]Area= Length \times Width[/tex]

[tex]Area= (x + 5) \times (x + 6)[/tex]

Open brackets

[tex]Area= x^2 + 5x + 6x + 30[/tex]

[tex]Area= x^2 + 11x + 30[/tex]

From the question, we understand that the area of the sheet is [tex]72cm^2[/tex]

So, the equation becomes

[tex]x^2 + 11x + 30 = 72[/tex]

Subtract 72 from both sides

[tex]x^2 + 11x + 30 -72= 0[/tex]

[tex]x^2 + 11x -42= 0[/tex]

Hence,

[tex](e)\ x^2 + 11x -42= 0[/tex] can be used to calculate the value of x