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While constructing a square root spiral, a student takes the previous hypotenuse as one side and 1 unit as the other side of each new right triangle. If the previous hypotenuse is \(\sqrt{5}\) units, what will be the length of the new hypotenuse?एक विद्यार्थी ने वर्गमूल सर्पिल बनाते समय प्रत्येक नया समकोण त्रिभुज पिछले कर्ण को एक भुजा और 1 इकाई को दूसरी भुजा लिया। यदि पिछले कर्ण की लंबाई \(\sqrt{5}\) इकाई है, तो नए कर्ण की लंबाई क्या होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\sqrt{6}\)\(\sqrt{6}\)
For the new right triangle, hypotenuse² = \((\sqrt{5})^2+1^2=5+1=6\). Hence the new hypotenuse is \(\sqrt{6}\) units. \(\sqrt{10}\) would result if the other side were also \(\sqrt{5}\). Exam tip: square the radical before applying Pythagoras’ theorem.नए समकोण त्रिभुज में कर्ण² = \((\sqrt{5})^2+1^2=5+1=6\)। इसलिए नया कर्ण \(\sqrt{6}\) इकाई होगा। \(\sqrt{10}\) तब मिलता यदि दूसरी भुजा भी \(\sqrt{5}\) होती। परीक्षा में पहले कर्ण का वर्ग लिखकर जोड़ें।
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