Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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A square sheet of paper measures 25 centimeters on each side. What is the length of the diagonal of this paper?
![**Problem:**
Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding if necessary to the nearest tenth.
5) A square sheet of paper measures 25 centimeters on each side. What is the length of the diagonal of this paper?
Options:
- A) 1250 cm
- B) 50 cm
- C) 25 cm
- D) 35.4 cm
**Explanation:**
To find the diagonal of a square, use the Pythagorean Theorem, \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the sides and \( c \) is the diagonal.
For a square, \( a = b = 25 \) cm.
Calculate:
\[ 25^2 + 25^2 = c^2 \]
\[ 625 + 625 = c^2 \]
\[ 1250 = c^2 \]
\[ c = \sqrt{1250} \]
Using a calculator, find:
\[ c \approx 35.4 \, \text{cm} \]
Thus, the length of the diagonal of the paper is approximately 35.4 cm, corresponding to option D).](https://content.bartleby.com/qna-images/question/f483ac81-a559-4957-8a20-1341dbf0c651/d03cf024-e049-4baa-baa9-929eee36909d/nsjnbpb_processed.jpeg)
Transcribed Image Text:**Problem:**
Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding if necessary to the nearest tenth.
5) A square sheet of paper measures 25 centimeters on each side. What is the length of the diagonal of this paper?
Options:
- A) 1250 cm
- B) 50 cm
- C) 25 cm
- D) 35.4 cm
**Explanation:**
To find the diagonal of a square, use the Pythagorean Theorem, \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the sides and \( c \) is the diagonal.
For a square, \( a = b = 25 \) cm.
Calculate:
\[ 25^2 + 25^2 = c^2 \]
\[ 625 + 625 = c^2 \]
\[ 1250 = c^2 \]
\[ c = \sqrt{1250} \]
Using a calculator, find:
\[ c \approx 35.4 \, \text{cm} \]
Thus, the length of the diagonal of the paper is approximately 35.4 cm, corresponding to option D).
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