Answer

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**Hint:**Here we will first find the breadth of the rectangle by using the area of rectangle formula. Then we will draw our rectangle and form a triangle in it. Finally we will use Pythagora's theorem and substitute the values of length and breadth as perpendicular and base to find the diagonal and get the required answer.

**Formula Used:**

We will use the following formulas:

1. Area of rectangle \[ = l \times b\], where $l$ is the length of the rectangle and $b$ is the breadth of the rectangle

2. Pythagoras Theorem: ${{P}^{2}}+{{B}^{2}}={{H}^{2}}$, where \[P\] is the perpendicular, \[B\] is the base and \[H\] is the hypotenuse of the right angled triangle.

**Complete step-by-step answer:**

It is given that:

The length of the rectangle \[ = 16\] cm

The Area of the rectangle \[ = 192\] sq. cm

We know that Area of rectangle \[ = l \times b\]

Substituting these values in the above formula, we get

\[ \Rightarrow 192 =16 \times b\]

Dividing both sides by 16, we get

\[ \Rightarrow b = \dfrac{{192}}{{16}}\]

\[ \Rightarrow b = 12\] cm….\[\left( 1 \right)\]

Now, we will draw the rectangle by using the above data.

Now we will use Pythagoras theorem to find the length of the diagonal.

In $\vartriangle ABD$,

\[A{B^2} + A{D^2} = B{D^2}\]

Substituting the value from the diagram in above formula, we get

\[ \Rightarrow {\left( {16} \right)^2} + {\left( {12} \right)^2} = B{D^2}\]

Applying the exponent on the terms, we get

\[ \Rightarrow 256 + 144 = B{D^2}\]

Adding the terms, we get

\[ \Rightarrow B{D^2} = 400\]

Taking square root on both sides, we get

\[ \Rightarrow BD = \sqrt{400}\]

\[ \Rightarrow BD = 20 \] cm

**So, we get the length of the diagonal as 20 cm.**

**Note:**

Rectangle is a quadrilateral having four sides with four right angles. It is a special case of a parallelogram which has a pair of adjacent sides in a perpendicular angle. Some properties of a rectangle are:

1. It is cyclic as all corners lie on a single circle.

2. It is equiangular as the angles in all corners are equal.

3. It has two lines reflection symmetry and rotational symmetry which are in order 2.

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