Question

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

Answer 1

The right equation will be "
`x^2+15x-54 =0`".

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:

⇒
`(x+3+4)`

`(x+7)`

and

⇒
`(x+4+4)`

`(x+8)`

now,

⇒
`(x+7)(x+8)=110`

⇒
`x^2+7x+8x+56=110`

⇒
`x^2+15+56=110`

On subtracting "56" from both sides, we get

⇒
`x^2+15x-56=110-56`

⇒
`x^2+15x=54`

Or,

⇒
`x^2+15x-54=0`