Let ABCD be a tetrahedron such that the edges | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the lengths of the edges $AB, AC$ and $AD$ be $c, b$ and $d$ respectively. Since the edges are mutually perpendicular,the areas of the triangl

Vedclass · Accepted Answer

$\sqrt{110}$

Vedclass · Answer

(C) Let the lengths of the edges $AB, AC$ and $AD$ be $c, b$ and $d$ respectively. Since the edges are mutually perpendicular,the areas of the triangles are given by: $Ar(	riangle ABC) = \frac{1}{2} bc = 5 \implies bc = 10$ $Ar(	riangle ACD) = \frac{1}{2} bd = 6 \implies bd = 12$ $Ar(	riangle ADB) = \frac{1}{2} cd = 7 \implies cd = 14$ By the projection theorem for a tetrahedron with a right-angled corner at $A$,the area of the face opposite to the right-angled corner is given by: $Ar(	riangle BCD) = \sqrt{(Ar(	riangle ABC))^2 + (Ar(	riangle ACD))^2 + (Ar(	riangle ADB))^2}$ $Ar(	riangle BCD) = \sqrt{5^2 + 6^2 + 7^2}$ $Ar(	riangle BCD) = \sqrt{25 + 36 + 49}$ $Ar(	riangle BCD) = \sqrt{110}$

Let $ABCD$ be a tetrahedron such that the edges $AB, AC$ and $AD$ are mutually perpendicular. Let the areas of the triangles $ABC, ACD$ and $ADB$ be $5, 6$ and $7$ square units respectively. Then the area (in square units) of the $\triangle BCD$ is equal to :

Similar Questions

Find the point in the $XY$-plane which is equidistant from the three points $A(2, 0, 3)$,$B(0, 3, 2)$,and $C(0, 0, 1)$.

If $A(0,1,2)$,$B(2,-1,3)$,and $C(1,-3,1)$ are the vertices of a triangle,then the distance between its circumcentre and orthocentre is

The transformed equation of $2x^2 + 3y^2 - z^2 - 8x + 18y + 2z + 9 = 0$ when the axes are translated to the point $(2, -3, 1)$ is

The edge of a cube is of length $a$. Then the shortest distance between the diagonal of a cube and an edge skew to it is:

Find the length of the perpendicular drawn from the point $P(2\hat{i} - \hat{j} + 5\hat{k})$ to the line $\vec{r} = (11\hat{i} - 2\hat{j} - 8\hat{k}) + \lambda(10\hat{i} - 4\hat{j} - 11\hat{k})$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module