A rectangular photograph is mounted on a rectangular card. There is a border ofequal width around the photograph. The perimeter of the card is 40 centimeters longer than that of the photograph. Find the width of the border in centimeters.
Let's assume the width of the photograph is 'x' centimeters.
The length of the photograph can then be represented as 'x + 2b', where 'b' is the width of the border.
The width of the card will be 'x + 2b + 2b' (border on both sides), which simplifies to 'x + 4b'.
The perimeter of the card is given as 40 centimeters longer than that of the photograph:
Perimeter of card = Perimeter of photograph + 40
2(x + 4b) + 2(x + 2b) = 2(x + x + 2b) + 40
We simplify the equation:
2x + 8b + 2x + 4b = 2x + 2x + 4b + 40
4x + 12b = 4x + 4b + 40
We can then cancel out the '4x' terms:
12b = 4b + 40
Subtracting '4b' from both sides:
12b - 4b = 40
Simplifying further:
8b = 40
Finally, divide both sides by 8:
b = 40/8
Therefore, the width of the border is 5 centimeters.
To solve this problem, we can set up equations based on the given information.
Let's assume the width of the photograph is "w" centimeters and the length of the photograph is "l" centimeters.
Since there is a border of equal width surrounding the photograph, the total width of the card would be "w + 2b" centimeters (where "b" is the width of the border) and the total length of the card would be "l + 2b" centimeters.
The perimeter of the photograph would be 2w + 2l centimeters, and the perimeter of the card would be 2(w + 2b) + 2(l + 2b) centimeters.
According to the given information, the perimeter of the card is 40 centimeters longer than that of the photograph. Therefore, we can set up the equation:
2(w + 2b) + 2(l + 2b) = 2w + 2l + 40
Simplifying the equation:
2w + 4b + 2l + 4b = 2w + 2l + 40
Cancelling out like terms:
4b + 4b = 40
8b = 40
Dividing both sides of the equation by 8:
b = 5
Therefore, the width of the border is 5 centimeters.
Let the width of the border be x cm. Since you are given a correlation between 2 different-sized perimeters, you will have to add 8 of the widths together:
8x = 40
x = 5 cm
Drawing it out will help.