Respuesta :
Answer:
Width of T.V. is 21.94 inches Height is 39 inches and area is 855.66 square inch.
Step-by-step explanation:
When we buy an electronic item like T.V or Blue Ray aspect ratio is the term which is used by the salesmen or technicians. Aspect ratio is actually the ratio of length and breadth of the screen of a device or ration of width and height.
In this question aspect ratio of television is given as 16:9
This can be written as [tex]\frac{W}{H}=\frac{16}{9}[/tex] or [tex]W=\frac{16}{9} H[/tex]
Screen of the T.V. is 65 inch which is the diagonal length of the screen.
We know from pythagoras theorem in a right angle triangle
[tex](diagonal)^{2}=(base)^2+(height)^2[/tex]
[tex](65)^2=(Base)^2+(height)^2[/tex]
[tex](65)^2= W^2+H^2 = (\frac{16}{9}H)^2+H^2[/tex]
[tex](65)= \sqrt{\frac{16}{9}H^2+H^2}\\ 65=H\sqrt{\frac{16}{9}+1}\\ 65=H\sqrt{\frac{25}{9}}\\ 65=\frac{5}{3}H\\ H=39 inches[/tex]
Now height of the T.V.will be
[tex]\frac{W}{H}=\frac{16}{9} \\\\\frac{H}{W}=\frac{9}{16}\\ H=\frac{9}{16}W = (\frac{9}{16})39= 21.94 Inches[/tex]
now area of the T.V.=W×H=39×21.94=855.66 square inch
Answer:
w = 56.65 in; h = 31.87 in; A = 1805 in²
Step-by-step explanation:
The aspect ratio of 16:9 tells us that w:h = 16:9 .
Let w = 16x and h = 9x.
The 65 in measurement is the diagonal length of the screen.
According to Pythagoras,
( 16x)² + (9x)² = 65²
256x² + 81x² = 4225 Combine like terms
337x² = 4225 Divide each side by 337
x² = 12.54 Take the square root of each side
x = 3.541 in
w = 16 × 3.541
w = 56.65 in
h = 9 × 3.541
h = 31.87 in
A = wh
A = 56.65 × 31.87
A = 1805 in²
