MCQ
The three different face diagonals of a cuboid (rectangular parallelopiped) have lengths $39,40,41$. The length of the main diagonal of the cuboid which joins a pair of opposite corners is
- ✓$49$
- B$49 \sqrt{2}$
- C$60$
- D$60 \sqrt{2}$
✓
Answer
Correct option: A.
$49$
a
(a)
(a)
Let the length, breadth and height of cuboid is $l, b$ and $h$ respectively.
$Given, l^2+h^2=39^2$
$\Rightarrow b^2+h^2=40^2$
$\Rightarrow \quad l^2+b^2=41^2$
$\Rightarrow \quad 2\left(l^2+b^2+h^2\right)=39^2+40^2+41^2$
$\Rightarrow \quad l^2+b^2+h^2=2401$
$\therefore$ Length of longest diagonal
$=\sqrt{l^2+b^2+h^2}$
$=\sqrt{2401}=49$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A variable circle is drawn passing through the origin $'O'.$ It intersects $X\, \& \,Y$ axis respectively at points $A\, \& \,B$ such that $OA + 2OB = K$ (non zero constant), then circle always passes through a fixed point $P$ other than origin. $P$ lies on -
→Given the inverse trigonometric function assumes principal values only. Let $x, y$ be any two real numbers in $[–1,1]$ such that $\cos ^{-1} x -\sin ^{-1} y =\alpha, \frac{-\pi}{2} \leq \alpha \leq \pi$.Then, the minimum value of $x^2+y^2+2 x y \sin \alpha$ is
→If $A \cap B = B$, then
→A test consists of $6$ multiple choice questions, each having $4$ alternative ans wers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is
→Inverse of the function $y = 2x - 3$ is
→ $(i)$ $f (x)$ is continuous and defined for all real numbers
→$(ii)$ $f '(-5) = 0 \,; \,f '(2)$ is not defined and $f '(4) = 0$
$(iii)$ $(-5, 12)$ is a point which lies on the graph of $f (x)$
$(iv)$ $f ''(2)$ is undefined, but $f ''(x)$ is negative everywhere else.
$(v)$ the signs of $f '(x)$ is given below
On the possible graph of $y = f (x)$ we have 
Let $y = {x^2}{e^{ - x}}$, then the interval in which $y $ increases with respect to $x$ is
→$\tan 75^\circ - \cot 75^\circ = $
→$\int_{}^{} {\frac{{dx}}{{\sqrt {1 + x} + \sqrt x }} = } $
→The number of real solutions of ${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = \frac{\pi }{2}$ is
→