The areas of three adjacent faces of a cuboid are $x, y$ and $z.$ If its volume is $V$,then which is true?

$A$ circular wire of length $168 \text{ cm}$ is cut and bent in the form of a rectangle whose sides are in the ratio of $5:7$. What is the length (in $\text{cm}$) of the diagonal of the rectangle?

The length of a rectangle is increased by $33.33 \%$. By what percent should the width be decreased to maintain the same area? (in $\%$)

The area of a square is $1024\, cm^2$. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is $12\, cm$ less than the side of this square?

The difference between two parallel sides of a trapezium is $4\, cm$. The perpendicular distance between them is $19\, cm$. If the area of the trapezium is $475\, cm^2$,find the length of the parallel sides.

What is the area of a given right-angled triangle?
$I.$ The length of the hypotenuse is $5\, cm$.
$II.$ The perimeter of the triangle is four times that of its base.
$III.$ One of the angles of the triangle is $60^{\circ}$.