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A square photograph is printed on a larger rectangular sheet of paper leaving a border around the photograph of 3 centimeters on the top and 4 centimeters on each of the remaining sides. The sheet of paper has an area of 110 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?
A. x^2 + 11x - 42 = 0
B. x^2 - 42 = 0
C. x^2 + 9x - 52 = 0
D. 11x - 42 = 0
E. x^2 - 11x - 42 = 0

Respuesta :

Cricetus

Answer:

The right equation will be "[tex]x^2+15x-54 =0[/tex]".

Step-by-step explanation:

According to the question,

Border around the photograph on the top is:

= 3 cm

The remaining sides,

= 4 cm

Area,

= 10 square cm

Let the length of sides be "x".

Since,

The paper's dimensions will be:

⇒ [tex](x+3+4)[/tex]

    [tex](x+7)[/tex]

and

⇒ [tex](x+4+4)[/tex]

    [tex](x+8)[/tex]

now,

⇒ [tex](x+7)(x+8)=110[/tex]

⇒ [tex]x^2+7x+8x+56=110[/tex]

⇒         [tex]x^2+15+56=110[/tex]

On subtracting "56" from both sides, we get

⇒       [tex]x^2+15x-56=110-56[/tex]  

⇒               [tex]x^2+15x=54[/tex]

Or,

⇒       [tex]x^2+15x-54=0[/tex]

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