Question

In a square box, a glass is to be surrounded by a 2 cm glass border. If the total area of the square is $121c{m^2}$. Find the dimension of the glass box.
A. 5 cm
B. 6 cm
C. 7 cm
D. 8 cm

Answer 1

Hint - In order to solve this problem we need consider the increment in both sides of glass by assuming the variable for length of the side of the glass and then equate the area of the glass box with the given area to get the side of the glass box.

Complete step-by-step answer:
Let x be the side of the glass.
We need to increase its length by 2 cm twice since we need the border of two centimetres.
So, the length of one of the sides will be x + 2 + 2 = x + 4
Then the length of the other side will also be x + 4.
Then the area will be (x + 4)(x + 4)
So, we can do (x + 4)(x + 4) = 121 (The give area is 121sqcm)
On solving further we get,
$
  {{\text{x}}^{\text{2}}}{\text{ + 8x + 16 = 121}} \\
  {{\text{x}}^{\text{2}}}{\text{ + 8x - 105 = 0}} \\
  {{\text{x}}^{\text{2}}}{\text{ + 15x - 7x - 105 = 0}} \\
  {\text{x(x + 15) - 7(x + 15) = 0}} \\
  {\text{(x - 7)(x + 15) = 0}} \\
$
Hence we can say that x = -15 or x = 7.
But length cannot be negative so the value of x is 7cm.
Therefore the length of the side of the glass is 7 cm.
Hence, the correct option is C.

Note – In order to get such problems correct we always need to think of dimensions from where it will be increasing or decreasing and from which amount we need to increase or decrease the length of the side. Knowing this and solving like solved above you will be getting the right answer.