Final answer:
To find the area of a 47" TV with an aspect ratio of 4:3, the width and height are determined using the aspect ratio and diagonal length. By applying the Pythagorean theorem, the area is calculated as 1060.32 square inches.
Step-by-step explanation:
To find the area of a 47" TV with an aspect ratio of 4:3, we must first determine the dimensions of the TV screen that correspond to this diagonal measurement and aspect ratio. The aspect ratio tells us that for every 4 units of width, there are 3 units of height. Using the Pythagorean theorem, we set up an equation with the width as 4x and the height as 3x where x is a constant. Then, by applying the diagonal measurement of the TV, we calculate x, find the width and height, and subsequently compute the area.
Let’s denote the width as W and the height as H. Given that the ratio is 4:3, we can write W as 4x and H as 3x. The relationship between the width, height, and diagonal is given by the Pythagorean theorem:
W^2 + H^2 = Diagonal^2
(4x)^2 + (3x)^2 = 47^2
16x^2 + 9x^2 = 47^2
25x^2 = 47^2
x^2 = (47^2) / 25
x^2 = 2209 / 25
x^2 = 88.36
x = √(88.36)
x ≈ 9.4
Now we have the values of W and H:
W = 4x = 4(9.4) ≈ 37.6"
H = 3x = 3(9.4) ≈ 28.2"
Finally, we find the area (A) by multiplying the width and the height:
A = W x H ≈ 37.6" x 28.2" ≈ 1060.32 square inches.
Therefore, the area of the TV is approximately 1060.32 square inches, which corresponds to answer choice D.