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Answer :
To determine the appropriate size of the television in inches, we need to find the diagonal measurement of the space available for it. Here's how you can do it step by step:
1. Understanding the Conversion:
- We know that 1 inch is equal to 2.54 centimeters.
2. Given Measurements:
- The space available for the television is given as 96 cm in width and 79 cm in height.
3. Convert the Width and Height to Inches:
- Convert the width from centimeters to inches:
[tex]\[
\text{Width in inches} = \frac{96 \, \text{cm}}{2.54 \, \text{cm/inch}} \approx 37.80 \, \text{inches}
\][/tex]
- Convert the height from centimeters to inches:
[tex]\[
\text{Height in inches} = \frac{79 \, \text{cm}}{2.54 \, \text{cm/inch}} \approx 31.10 \, \text{inches}
\][/tex]
4. Calculate the Diagonal:
- Use the Pythagorean theorem to find the diagonal in inches. The formula for the diagonal [tex]\(d\)[/tex] of a rectangle is:
[tex]\[
d = \sqrt{(\text{Width in inches})^2 + (\text{Height in inches})^2}
\][/tex]
- Substitute the width and height:
[tex]\[
d = \sqrt{(37.80)^2 + (31.10)^2} \approx 48.95 \, \text{inches}
\][/tex]
5. Conclusion:
- Thus, the television should have a diagonal measurement of approximately 48.95 inches to fit perfectly in the given space.
1. Understanding the Conversion:
- We know that 1 inch is equal to 2.54 centimeters.
2. Given Measurements:
- The space available for the television is given as 96 cm in width and 79 cm in height.
3. Convert the Width and Height to Inches:
- Convert the width from centimeters to inches:
[tex]\[
\text{Width in inches} = \frac{96 \, \text{cm}}{2.54 \, \text{cm/inch}} \approx 37.80 \, \text{inches}
\][/tex]
- Convert the height from centimeters to inches:
[tex]\[
\text{Height in inches} = \frac{79 \, \text{cm}}{2.54 \, \text{cm/inch}} \approx 31.10 \, \text{inches}
\][/tex]
4. Calculate the Diagonal:
- Use the Pythagorean theorem to find the diagonal in inches. The formula for the diagonal [tex]\(d\)[/tex] of a rectangle is:
[tex]\[
d = \sqrt{(\text{Width in inches})^2 + (\text{Height in inches})^2}
\][/tex]
- Substitute the width and height:
[tex]\[
d = \sqrt{(37.80)^2 + (31.10)^2} \approx 48.95 \, \text{inches}
\][/tex]
5. Conclusion:
- Thus, the television should have a diagonal measurement of approximately 48.95 inches to fit perfectly in the given space.
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