Let `A B C D` be a tetrahedron such that the edges `A B ,A Ca n dA D` are mutually perpendicular. Let the area of triangles `A B C ,A C Da n dA D B` be 3, 4 and 5sq. units, respectively. Then the area of triangle `B C D` is `5sqrt(2)` b. `5` c. `(sqrt(5))/2` d. `5/2`

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

The diagonals of quadrilateral A B C D , A C a n d B D intersect in Odot Prove that if B O=O D , the triangles A B C a n d A D C are equal in area.

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

A and B are isotopes. B and C are isobars. If d_A, d_B " and " d_C be the densities of nuclei A, B and C respectively then

In the given figure, A B C D is a rectangle with A D=4 units and A E=E BdotE F is perpendicular to D B and is half of D F . If the area of the triangle D E F is 5 sq. units, then what is the area of A B C D ? 18sqrt(3) sq. units (b) 20 sq. units (c) 24 sq. units (d) 28 sq. units

In quadrilateral A B C D show in Figure. A B D C a n d A D_|_A Bdot Also, A B=8m , D C=B C=5mdot Find the area of the quadrilateral.

A B C is a triangle in which D is the mid-point of B C ,\ E\ a n d\ F are mid-points of D C\ a n d\ A E respectively. If area of A B C is 16\ c m^2, find the area of D E F

In A B C ,/_A=90^0a n dA D is an altitude. Complete the relation (B D)/(D A)=(A B)/(()) .

If A(1,-1,2),B(2,1,-1)C(3,-1,2) are the vertices of a triangle then the area of triangle ABC is (A) sqrt(12) (B) sqrt(3) (C) sqrt(5) (D) sqrt(13)

A B C D is a cyclic quadrilateral whose diagonals A Ca n dB D intersect at P . If A B=D C , Prove that : P A B~= P D C P A=P Da n dP C=P B A D B C