Question

example 2
a big-screen tv has an aspect ratio of 16:9, which means that for every 16 inches of
width, the tv is 9 inches high. what is the height of a tv that is 40 inches wide?

solution
set up a proportion to solve for x, the height of the tv.

\\(\frac{40}{x} = \frac{16}{9}\\)

\\(9 \times x \times \frac{40}{x} = \frac{16}{9} \times x \times 9\\) multiply by a common factor.

\\(9 \times 40 = 16x\\) simplify.

\\(\frac{9 \times 40}{16} = x\\)

\\(22.5 = x\\)

the tv will be 22.5 inches wide.

Explanation:

Step1: Set up the proportion

Let \( x \) be the height of the TV. The aspect ratio is \( 16:9 \), so for a width of 40 inches, we set up the proportion \(\frac{40}{x}=\frac{16}{9}\).

Step2: Cross - multiply

Multiply both sides of the equation \(\frac{40}{x}=\frac{16}{9}\) by \( 9x \) (the product of the denominators) to get \( 9\times40 = 16x \).

Step3: Solve for \( x \)

Divide both sides of the equation \( 9\times40 = 16x \) by 16. So \( x=\frac{9\times40}{16}\). Calculate \( 9\times40 = 360 \), then \( x=\frac{360}{16}=22.5 \).

Answer:

The height of the TV is \( 22.5 \) inches.