To find the height of each screen, we can use the Pythagorean Theorem. The relationship can be expressed as follows:
\[ d^2 = w^2 + h^2 \]
where \( d \) is the diagonal, \( w \) is the width, and \( h \) is the height. We can rearrange the equation to solve for height:
\[ h = \sqrt{d^2 - w^2} \]
Now we will calculate the height for each screen:
Screen A:
- Diagonal = 15 inches
- Width = 13 inches
\[ h = \sqrt{15^2 - 13^2} = \sqrt{225 - 169} = \sqrt{56} \approx 7.48 \text{ inches} \]
Screen B:
- Diagonal = 22 inches
- Width = 19 inches
\[ h = \sqrt{22^2 - 19^2} = \sqrt{484 - 361} = \sqrt{123} \approx 11.09 \text{ inches} \]
Screen C:
- Diagonal = 32 inches
- Width = 28 inches
\[ h = \sqrt{32^2 - 28^2} = \sqrt{1024 - 784} = \sqrt{240} \approx 15.49 \text{ inches} \]
Screen D:
- Diagonal = 40 inches
- Width = 35 inches
\[ h = \sqrt{40^2 - 35^2} = \sqrt{1600 - 1225} = \sqrt{375} \approx 19.36 \text{ inches} \]
Now let's summarize the results in a table:
| Screen | Diagonal (inches) | Width (inches) | Height (inches) | |--------|-------------------|----------------|------------------| | A | 15 | 13 | 7.48 | | B | 22 | 19 | 11.09 | | C | 32 | 28 | 15.49 | | D | 40 | 35 | 19.36 |
Next, we determine which screen fits Yoselin's shelf, knowing that the maximum height is 17 inches and maximum width is 50 inches:
- Screen A: Height = 7.48 inches (Fits)
- Screen B: Height = 11.09 inches (Fits)
- Screen C: Height = 15.49 inches (Fits)
- Screen D: Height = 19.36 inches (Does not fit)
Among the screens that fit, the largest screen in terms of diagonal is Screen C at 32 inches.
Thus, the largest screen that will fit on Yoselin’s shelf is Screen C (32 inches).
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