Question
A certain television is advertised as a 38 -inch TV (the diagonal length). If the height of the TV is 25 inches, how wide is the TV? Round to the nearest tenth of an inch.
Ask by Henry Edwards. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The TV is approximately 28.6 inches wide.
Solution
To find the width of the TV, we can use the Pythagorean theorem since we have the diagonal length and the height of the TV.
Given:
- Diagonal length (d) = 38 inches
- Height (h) = 25 inches
We can use the Pythagorean theorem to find the width (w):
\[ d^2 = h^2 + w^2 \]
Substitute the given values:
\[ 38^2 = 25^2 + w^2 \]
Solve for w:
\[ 1444 = 625 + w^2 \]
\[ w^2 = 1444 - 625 \]
\[ w^2 = 819 \]
\[ w = \sqrt{819} \]
Now, we can calculate the width of the TV by finding the square root of 819 and rounding it to the nearest tenth of an inch.
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{819}\)
- step1: Write as a product:
\(\sqrt{9\times 91}\)
- step2: Write in exponential form:
\(\sqrt{3^{2}\times 91}\)
- step3: Use the properties of radicals:
\(\sqrt{3^{2}}\times \sqrt{91}\)
- step4: Simplify the root:
\(3\sqrt{91}\)
The width of the TV is approximately 28.6 inches when rounded to the nearest tenth of an inch.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the width of the TV, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides (the height and width). Here, we have the diagonal as 38 inches and the height as 25 inches. Using the formula \(a^2 + b^2 = c^2\), we set \(c = 38\) (the diagonal), and \(a = 25\) (the height). We need to find \(b\) (the width): \[ 25^2 + b^2 = 38^2 \] \[ 625 + b^2 = 1444 \] \[ b^2 = 1444 - 625 \] \[ b^2 = 819 \] \[ b = \sqrt{819} \approx 28.6 \] So, the width of the TV is approximately 28.6 inches.
