Question : The breadth ‘b’ of a room is twice its height and half of its length. Find the length of the longest diagonal of the room.
Option 1: $\frac{\sqrt{20} \mathrm{~b}}{2}$
Option 2: $\frac{\mathrm{b}}{2}$
Option 3: $\frac{\sqrt{21} \mathrm{~b}}{2}$
Option 4: $\frac{\sqrt{19} \mathrm{~b}}{2}$
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Correct Answer: $\frac{\sqrt{21} \mathrm{~b}}{2}$
Solution : According to the question, b = 2 × height ⇒ Height = $\frac{1}{2}$b Also, b = $\frac12\times$length ⇒ Length = 2b Length of the diagonal $=\sqrt{l^2+b^2+h^2}$ $=\sqrt{(2b)^2+b^2+(\frac12b)^2}$ $=\sqrt{4b^2+b^2+\frac {b^2}{4}}$ $=\sqrt{\frac{16b^2+4b^2+b^2}{4}}$ $=\sqrt{\frac{21b^2}{4}}$ $=\frac{\sqrt{21}b}{2}$ Hence, the correct answer is $\frac{\sqrt{21}b}{2}$.
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Question : If $\mathrm{p}=\frac{\sqrt{2}+1}{\sqrt{2}-1}$ and $\mathrm{q}=\frac{\sqrt{2}-1}{\sqrt{2}+1}$ then, find the value of $\frac{\mathrm{p}^2}{\mathrm{q}}+\frac{\mathrm{q}^2}{\mathrm{p}}$.
Question : The length of the longest diagonal of a cube is $7 \sqrt{3}$ cm. Find its volume (in cm3).
Question : The volume of a cone with a height equal to the radius and slant height of 5 cm is:
Question : The length of each side of a triangle is 12 cm. What is the length of the circumradius of the triangle?
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