Question

In the given figure, ABCD is a rhombus. If OB = 3 units, OC = 4 units and AE = 6.4 units. Find the length of BE.

• A. 0.4 units
• B. 0.8 units
• C. 1.4 units
• D. 1.6 units

Answer 1

The correct option is C

1.4 units

Since, diagonals of a rhombus intersect at ${90}^{\circ }$,$\Delta BOC$ is a right angled triangle.
So, using Pythagoras theorem
$O{B}^2$ + $O{C}^2$ = $B{C}^2$
$BC=\sqrt{3^2+4^2}$ = $\sqrt{9+16}$
$BC=\sqrt{25}$ = 5 units
AE = AB + BE
In a rhombus all the sides are equal. So AB = BC = 5 units.
$\therefore$ BE = AE - AB
= 6.4 - 5
= 1.4 units