Answer

Verified

340.2k+ views

**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.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE