Question 584744: A TV screen is 40in high and 60in long. Using the vetical and horizontal control buttons, the picture is compressed to 62.5% of its original area, leaving a uniform dark strip around the outside. Find the dimensions of the smaller picture.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! original dimensions are 40 * 60 for an area of 2400 square inches.
the area is reduced to 62.5% of its original area.
this makes the near area equal to .625 * 2400 = 1500.
if we let x equal the height and y equal the length, then we get:
x * y = 1500
since we know that the length to height ratio is 60/40 = 3/2, we can set the length equal to 3/2 * the height.
since x equals the height and y equals the length, this means that:
y = 3/2 * x
in our equation of x * y = 1500, we replace y with 3/2 * x to get:
x * 3/2 * x = 1500 which simplifies to:
3/2 * x^2 = 1500
multiply both sides of this equation by 2/3 to get:
x^2 = 1500 * 2/3 which simplifies to:
x^2 = 1000.
solve for x to get x = 31.6227766
since x = 31.6227766, and y = 3/2 * x, we can solve for y to get:
y = 3/2 * 31.6227766 which is equal to:
y = 47.4341649
we now have the new dimensions of the screen assuming the same viewing ratio as the original screen.
those new dimensions are:
height = 47.4341649 inches
width = 31.6227766
the new area is equal to height * width which is equal to:
47.4341649 * 31.6227766 which is equal to 1500 square inches, confirming the calculations are correct.
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