Answer :
Final answer:
To find the width of a 70" TV with a 16:9 aspect ratio, you can set up the proportion based on the aspect ratio, use the Pythagorean theorem with the diagonal length, and solve for the width. The width is approximately 61 inches.
Explanation:
To calculate the width of a 70" TV with an aspect ratio of 16:9, we need to use the aspect ratio as a guide. The aspect ratio 16:9 means that for every 16 units of width, there are 9 units of height. Since the diagonal measurement of the TV is 70 inches, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides (the width and height).
Firstly, set up the ratio 16/9 = width/height, and then we can express the height as (9/16)*width. Now, by the Pythagorean theorem:
(width)² + (height)² = (diagonal)²
Substituting height with (9/16)*width and diagonal with 70, we get:
(width)² + ((9/16)*width)² = 70²
Calculate the width using the equation derived from the aspect ratio and diagonal size:
(width)² + (81/256)*(width)² = 4900
Solving for width, we conclude that the width of the TV is approximately 61 inches.
Answer:
(C)61''
Step-by-step explanation:
Aspect ratio =Width: Height
If the TV has an aspect ratio of 16:9
Since the diagonal of the TV is 70 inches
[tex]\frac{Width}{Height}= \frac{16}{9}\\$Therefore:$\\Width= \dfrac{16}{9}Height[/tex]
Using Pythagoras Theorem
[tex]Diagonal^2=Width^2+Height^2\\70^2=Width^2+Height^2[/tex]
[tex]70^2=(\frac{16}{9}Height)^2+Height^2\\4900=\dfrac{256h^2+81h^2}{81} \\256h^2+81h^2=4900 \times 81\\337h^2=396900\\h^2=1177.74\\h=34.32''[/tex]
Therefore:
[tex]Width= \dfrac{16}{9} \times 34.32\\=61''[/tex]