The size of a television is given by the length of the diagonal of the screen. The ratio of the height to the width of wide flat-screen TV is 8:15. Find expressions for the width and height of a wide-screen TV in terms of the length of its diagonal.
using the ratios,
let the width be 8x
and the length be 15x
led d be the diagonal
d^2 = (8x)^2 + (15x)^2
= 64x^2 + 225x^2 = 289x^2
d = 17x
or x = d/17
width = 8x = 8d/17
length = 15x = 15d/17
Thank you
To find expressions for the width and height of a wide-screen TV in terms of the length of its diagonal, we need to use the given ratio of the height to the width.
Let's assume the width of the TV is x and the height is y.
According to the given ratio, y/x = 8/15.
Now, let's consider the diagonal as the hypotenuse of a right triangle. The height and the width of the TV are the other two sides. So, we can apply the Pythagorean theorem.
According to the Pythagorean theorem, (height)^2 + (width)^2 = (diagonal)^2.
Substituting the values, we get:
y^2 + x^2 = (diagonal)^2.
From the given ratio, we can express y in terms of x:
y = (8/15)x.
Substituting this value in the equation, we get:
(8/15)x^2 + x^2 = (diagonal)^2.
Combining like terms, we have:
(8/15 + 1)x^2 = (diagonal)^2.
Simplifying further, we get:
(23/15)x^2 = (diagonal)^2.
Dividing both sides by (23/15), we get:
x^2 = [(diagonal)^2 / (23/15)].
Taking the square root of both sides, we get:
x = sqrt[(diagonal)^2 / (23/15)].
Therefore, the expression for the width of the wide-screen TV in terms of the length of its diagonal is:
width = sqrt[(diagonal)^2 / (23/15)].
To find the expression for the height, substitute the value of x from the given ratio:
y = (8/15)x.
Therefore, the expression for the height of the wide-screen TV in terms of the length of its diagonal is:
height = (8/15) * sqrt[(diagonal)^2 / (23/15)].
To find expressions for the width and height of the wide flat-screen TV in terms of the length of its diagonal, we need to use the given ratio of the height to the width.
Let's assume that the height of the TV is represented by 'h' and the width of the TV is represented by 'w'.
We are given that the ratio of the height to the width is 8:15, so we can write:
h/w = 8/15
To find the expressions in terms of the length of the diagonal, we can make use of the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the TV represents the hypotenuse, and the height and width of the TV represent the other two sides of the right triangle.
Let the diagonal of the TV be represented by 'd'.
According to the Pythagorean theorem, we have:
d^2 = h^2 + w^2
Rearranging this equation, we get:
w^2 = d^2 - h^2
Now, substituting the value of h/w from the given ratio, we have:
w^2 = d^2 - (8/15)^2 * w^2
Expanding the right side of the equation, we get:
w^2 = d^2 - 64/225 * w^2
Combining like terms, we have:
w^2 + 64/225 * w^2 = d^2
Multiplying through by 225 to get rid of the fraction, we get:
225w^2 + 64w^2 = 225d^2
Simplifying, we have:
289w^2 = 225d^2
Taking the square root of both sides, we get:
w = (15/17) * d
Similarly, substituting the value of w in the equation h/w = 8/15, we have:
h/(15/17 * d) = 8/15
Multiplying both sides by (15/17 * d), we get:
h = (8/15) * (15/17) * d
Simplifying, we have:
h = (8/17) * d
Therefore, the expressions for the width (w) and height (h) of the wide flat-screen TV in terms of the length of its diagonal (d) are:
w = (15/17) * d
h = (8/17) * d