The size of a squre computer screen is measured by the length of its diagonal . How much bigger is the visible area of a square 24- inch screen than the area of a square 20-inch screen?

Answer

To find out how much bigger the visible area of a square 24-inch screen is compared to a square 20-inch screen, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side of a square
The diagonal \( d \) of a square is related to its side length \( s \) by the formula:
\[ d = s \sqrt{2} \]
From this, we can find the side length of the square by rearranging the formula:
\[ s = \frac{d}{\sqrt{2}} \]

### Step 2: Calculate the side length of the 24-inch screen
Using the diagonal of the 24-inch screen:
\[ s_{24} = \frac{24}{\sqrt{2}} = 24 \cdot \frac{\sqrt{2}}{2} = 12\sqrt{2} \text{ inches} \]

### Step 3: Calculate the area of the 24-inch screen
The area \( A \) of a square is given by:
\[ A = s^2 \]
So, for the 24-inch screen:
\[ A_{24} = (12\sqrt{2})^2 = 144 \cdot 2 = 288 \text{ square inches} \]

### Step 4: Calculate the side length of the 20-inch screen
Using the diagonal of the 20-inch screen:
\[ s_{20} = \frac{20}{\sqrt{2}} = 20 \cdot \frac{\sqrt{2}}{2} = 10\sqrt{2} \text{ inches} \]

### Step 5: Calculate the area of the 20-inch screen
For the 20-inch screen:
\[ A_{20} = (10\sqrt{2})^2 = 100 \cdot 2 = 200 \text{ square inches} \]

### Step 6: Find the difference in areas
Now, we need to find how much bigger the area of the 24-inch screen is compared to the 20-inch screen:
\[ \text{Difference} = A_{24} - A_{20} = 288 - 200 = 88 \text{ square inches} \]

### Final Answer
The visible area of the square 24-inch screen is 88 square inches bigger than that of the square 20-inch screen.

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