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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