when a television is advertised as a 27-inch model. the screen is a rectangle with a diagonal of 27 inches. The screen has a height of 15 inches. Find the length, to the nearest hundredth of an inch of the television?
If the length is x, then
x^2 + 15^2 = 27^2
right?
To find the length of the television, we can use the Pythagorean theorem since we know the diagonal and the height of the screen. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides (the height and the length in this case).
Let's denote the length of the TV as 'L'. We know that the height, which is one side of the right triangle, is 15 inches. The other side is the length 'L' that we want to find, and the diagonal is 27 inches.
Using the Pythagorean theorem, we have the equation:
L^2 + 15^2 = 27^2
Simplifying the equation:
L^2 + 225 = 729
L^2 = 729 - 225
L^2 = 504
To find the value of 'L', we take the square root of both sides:
L = √504
Calculating the square root of 504 gives us:
L ≈ 22.45 inches (rounded to the nearest hundredth of an inch)
Therefore, the length of the television is approximately 22.45 inches.