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In a square root spiral, a perpendicular segment of length \(1\) is drawn on the hypotenuse \(\sqrt{48}\). What is the new hypotenuse equal to (as a whole number)?वर्गमूल सर्पिल में कर्ण \(\sqrt{48}\) पर \(1\) लंबाई का एक लंबवत (perpendicular) खंड बनाया जाता है। नया कर्ण किस पूर्ण संख्या के बराबर होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 77
Using Pythagoras’ theorem, the new hypotenuse \(x\) satisfies:
\[
x^2=(\sqrt{48})^2+(1)^2=48+1=49.
\]
So \(x=\sqrt{49}=7\).पिथागोरस प्रमेय के अनुसार नया कर्ण \(x\) के लिए:
\[
x^2=(\sqrt{48})^2+(1)^2=48+1=49.
\]
अतः \(x=\sqrt{49}=7\) ।
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