Question

1. a 30 inch tv has an aspect ratio of 4:3. a tv that is 4 feet wide and 3 feet tall has a diagonal length of 5 ft. how can you use this information to figure out the width of the 30 inch tv? explain.

Explanation:

Step1: Define ratio variable

Let the width be $4x$ and height be $3x$.

Step2: Apply Pythagorean theorem

$$(4x)^2 + (3x)^2 = 30^2$$

Step3: Simplify the equation

$$16x^2 + 9x^2 = 900$$
$$25x^2 = 900$$

Step4: Solve for $x$

$$x^2 = \frac{900}{25} = 36$$
$$x = \sqrt{36} = 6$$

Step5: Calculate TV width

$$\text{Width} = 4x = 4 \times 6$$

Answer:

We use the 4:3 aspect ratio and the Pythagorean theorem (since TV size is the diagonal length). Let the width be $4x$ and height be $3x$. Substitute into the theorem: $(4x)^2 + (3x)^2 = 30^2$. Simplify to find $x=6$, so the width is $4\times6=24$ inches.
The width of the 30-inch TV is 24 inches.