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In the figure given above, a rectangular photograph is placed in a black frame that has a uniform width of x centimeters between the photograph and the outer boundary of the frame. If the difference between the perimeter of the photograph and of the outer boundary of the frame is 32 centimeters, what is the width in centimeters of the black frame?
  • a)
    2
  • b)
    4
  • c)
    8
  • d)
    12
  • e)
    16
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In the figure given above, a rectangular photograph is placed in a bla...
Given
  • Width of frame = x centimeters
  • Perimeter (Outer frame) - Perimeter(photograph) = 32
  • Let’s assume the length and breadth of the outer frame be l and b centimeters respectively.
To Find: Value of x?
 
Approach
  1. As we know that x is the distance between the photograph and the outer frame, we can find the dimensions of the photograph in terms of l, b and x.
  2. Now, we know that Perimeter of the outer frame = 2(l+b)
    1. We will then use the relation of difference in perimeters of the outer frame and the photograph to find the value of x.
Working out
  1. As the width of the frame is x centimeters, the length of the rectangular photograph = l - x - x = l +2x
    1. Similarly, the width of the frame = b - x - x = b -2x. 
  2. So, perimeter of the rectangular photograph = 2 (l +b -4x) = 2(l + b) - 8x
  3. Perimeter (Outer frame) – Perimeter(photograph) = 32
    a. 2(l + b)– 2(l + b) + 8x = 32
    b. 8x = 32
    c. x = 4 centimeters
Hence, the width of the frame is 4 centimeters
Answer : B
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In the figure given above, a rectangular photograph is placed in a black frame that has a uniform width of x centimeters between the photograph and the outer boundary of the frame. If the difference between the perimeter of the photograph and of the outer boundary of the frame is 32 centimeters, what is the width in centimeters of the black frame?a)2b)4c)8d)12e)16Correct answer is option 'B'. Can you explain this answer?
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