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Answer :
Sure, let's solve the problem step by step.
David wants to buy a TV that fits perfectly into a space that measures 96 cm by 79 cm. To find out the size of the TV needed in inches, we need to calculate the diagonal of this space in centimeters first and then convert it to inches.
### Step 1: Calculate the diagonal in centimeters
We can use the Pythagorean theorem to find the diagonal of a rectangle:
[tex]\[
\text{Diagonal} = \sqrt{\text{width}^2 + \text{height}^2}
\][/tex]
Here, the width is 96 cm and the height is 79 cm. Plugging these values into the formula, we get:
[tex]\[
\text{Diagonal} = \sqrt{96^2 + 79^2}
\][/tex]
Upon calculating the squares and the sum:
[tex]\[
96^2 = 9216
\][/tex]
[tex]\[
79^2 = 6241
\][/tex]
[tex]\[
\text{Sum} = 9216 + 6241 = 15457
\][/tex]
Then we calculate the square root:
[tex]\[
\text{Diagonal} = \sqrt{15457} \approx 124.33 \, \text{cm}
\][/tex]
### Step 2: Convert the diagonal from centimeters to inches
We know that:
[tex]\[
1 \, \text{inch} = 2.54 \, \text{cm}
\][/tex]
To convert the diagonal from centimeters to inches, we divide the length in centimeters by the number of centimeters per inch:
[tex]\[
\text{Diagonal in inches} = \frac{\text{Diagonal in centimeters}}{2.54}
\][/tex]
So, we have:
[tex]\[
\text{Diagonal in inches} = \frac{124.33}{2.54} \approx 48.95 \, \text{inches}
\][/tex]
Thus, the TV should have a diagonal of approximately 48.95 inches to fit into the space of 96 cm by 79 cm.
David wants to buy a TV that fits perfectly into a space that measures 96 cm by 79 cm. To find out the size of the TV needed in inches, we need to calculate the diagonal of this space in centimeters first and then convert it to inches.
### Step 1: Calculate the diagonal in centimeters
We can use the Pythagorean theorem to find the diagonal of a rectangle:
[tex]\[
\text{Diagonal} = \sqrt{\text{width}^2 + \text{height}^2}
\][/tex]
Here, the width is 96 cm and the height is 79 cm. Plugging these values into the formula, we get:
[tex]\[
\text{Diagonal} = \sqrt{96^2 + 79^2}
\][/tex]
Upon calculating the squares and the sum:
[tex]\[
96^2 = 9216
\][/tex]
[tex]\[
79^2 = 6241
\][/tex]
[tex]\[
\text{Sum} = 9216 + 6241 = 15457
\][/tex]
Then we calculate the square root:
[tex]\[
\text{Diagonal} = \sqrt{15457} \approx 124.33 \, \text{cm}
\][/tex]
### Step 2: Convert the diagonal from centimeters to inches
We know that:
[tex]\[
1 \, \text{inch} = 2.54 \, \text{cm}
\][/tex]
To convert the diagonal from centimeters to inches, we divide the length in centimeters by the number of centimeters per inch:
[tex]\[
\text{Diagonal in inches} = \frac{\text{Diagonal in centimeters}}{2.54}
\][/tex]
So, we have:
[tex]\[
\text{Diagonal in inches} = \frac{124.33}{2.54} \approx 48.95 \, \text{inches}
\][/tex]
Thus, the TV should have a diagonal of approximately 48.95 inches to fit into the space of 96 cm by 79 cm.
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