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The area of a rectangle lies between \( \Large \Large 40 cm^{2} \) and \( \Large \Large 45 cm^{2} \). If one of the sides is 5 cm, then its diagonal lies between
A) 8 cm and 10 cm
B) 9 cm and 11 cm
C) 10 cm and 12 cm
D) 11cm and 13 cm
Correct answer:
B) 9 cm and 11 cm
Description for Correct answer:
Area of rectangle lies between \( \Large 40 cm^{2}\)
and \( \Large 45 cm^{2}\).
Now, one side = 5 cm
Since, area cannot be less than \( \Large 40 cm^{2}\)
Hence, other side cannot be less than
= \( \Large \frac{40}{5} \) = 8 cm
Since, area cannot be greater than \( \Large 45 cm^{2}\)
Hence, other side cannot be greater than
= \( \Large \frac{45}{5} \) = 9 cm
Minimum value of diagonal
= \( \Large \sqrt{8^{2}+5^{2}}=\sqrt{89} \) =9.43cm
Maximum value of diagonal
= \( \Large \sqrt{9^{2}+5^{2}}=\sqrt{106} \) = 10.3cm
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