Question

The size of a flat-screen television is given as the length of the screen's diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?

• A. 106.75
• B. 213.5
• C. 427
• D. 729
• E. 1,156

Hint:

For square screens, the area is related to the diagonal by \( \text{side} = \frac{\text{diagonal}}{\sqrt{2}} \), and area is the side squared.

Answer 1

The Correct Option is B

Step 1: Calculate the area of the 34-inch television.
The area of a square is given by \( A = \text{side}^2 \). The diagonal of a square relates to its side by the Pythagorean theorem: \[ \text{diagonal} = \text{side} \times \sqrt{2}. \] For the 34-inch diagonal, the side length is: \[ \text{side} = \frac{34}{\sqrt{2}} \approx 24.04 \, \text{inches}. \] Thus, the area of the 34-inch square television is: \[ A_{34} = 24.04^2 \approx 578.92 \, \text{square inches}. \] Step 2: Calculate the area of the 27-inch television.
For the 27-inch diagonal, the side length is: \[ \text{side} = \frac{27}{\sqrt{2}} \approx 19.09 \, \text{inches}. \] Thus, the area of the 27-inch square television is: \[ A_{27} = 19.09^2 \approx 364.42 \, \text{square inches}. \] Step 3: Calculate the difference in areas.
The difference in area between the 34-inch and 27-inch televisions is: \[ \text{Difference} = 578.92 - 364.42 = 213.5 \, \text{square inches}. \] Step 4: Conclusion.
Thus, the difference in the areas of the two televisions is 213.5 square inches. The correct answer is (B) 213.5.