A page for a journal contains 70 square inches of type written words. The height of a page is twice the width. If the Margin around the type is to be 2 inches uniformly, what are the dimensions of a page?
H = 2W
70 = H * W = 2W * W = 3W
Solve for W then H. For 2 inch additional margin, add 4 inches to each (2 on each side).
I DO NOT KNOW THE ANSWER.
To find out the dimensions of the page, we can set up and solve an equation using the given information.
Let's assume the width of the page is x inches.
According to the given information, the height of the page is twice the width, so the height would be 2x inches.
The margin around the type is 2 inches on all sides, so each side of the type-written area is reduced by 4 inches (2 inches on each side). Therefore, the width of the type-written area would be (x - 4) inches, and the height would be (2x - 4) inches.
Given that the area of the type-written words is 70 square inches, we can set up the following equation:
(width of the type-written area) * (height of the type-written area) = 70 square inches
(x - 4) * (2x - 4) = 70
Expanding the equation:
2x^2 - 12x + 16 = 70
Rearranging the equation:
2x^2 - 12x + 16 - 70 = 0
Simplifying:
2x^2 - 12x - 54 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. After finding the values of x, we can use them to calculate the dimensions of the page.
Let's solve this equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case:
a = 2
b = -12
c = -54
Substituting the values into the quadratic formula:
x = (-(-12) ± √((-12)^2 - 4 * 2 * (-54))) / (2 * 2)
Simplifying:
x = (12 ± √(144 + 432)) / 4
x = (12 ± √576) / 4
x = (12 ± 24) / 4
We get two possible values for x:
x = (12 + 24) / 4 = 36 / 4 = 9
x = (12 - 24) / 4 = -12 / 4 = -3
The width of the page cannot be negative, so we discard the negative value of x.
Therefore, the width of the page is 9 inches.
Since the height of the page is twice the width, the height would be 2 * 9 = 18 inches.
Hence, the dimensions of the page are 9 inches (width) and 18 inches (height).