Question

If the length and diagonal of a rectangle are 143 m and 145 m, respectively, find its area
and perimeter.​

Answer 1

Required Answer :

The area of rectangle = 3432 m²

The perimeter of rectangle = 334 m

Given :

• Length of rectangle = 143 m

• Diagonal of rectangle = 145 m

To find :

• Area of rectangle

• Perimeter of rectangle

Solution :

Using formula,

• Diagonal of rectangle = √(l² + b²)

where,

• l denotes the length
• b denotes the breadth

Substituting the given values :-

→ 145 = √((143)² + b²)

Squaring both the sides :-

→ (145)² = (143)² + b²

→ 21,025 = 20,449 + b²

→ 21,025 - 20,449 = b²

→ 576 = b²

Taking square root on both the sides :-

→ √576 = b

→ √(24 × 24) = b

→ ± 24 = b

As we know, the breadth of the rectangle cannot be negative. So, the negative sign will get rejected.

→ ± 24 Reject -ve = b

→ 24 = b

Therefore, the breadth of rectangle = 24 m

Area of rectangle :-

Using formula,

• Area of rectangle = l × b

Substituting the given values :-

→ Area of rectangle = 143 × 24

→ Area of rectangle = 3432

Therefore, the area of rectangle = 3432 m²

Perimeter of the rectangle :-

Using formula,

• Perimeter of rectangle = 2(l + b)

Substituting the given values :-

→ Perimeter of rectangle = 2(143 + 24)

→ Perimeter of rectangle = 2(167)

→ Perimeter of rectangle = 334

Therefore, the perimeter of rectangle = 334 m

Answer 2

Answer:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Given:}}}}}}}\end{gathered}$

• $\red\bigstar$ Diagonal of Rectangle = 145 m
• $\red\bigstar$ Lenght of Rectangle = 143 m

$\begin{gathered} \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{To Find:}}}}}}}\end{gathered}$

• $\green\bigstar$ Breadth of Rectangle
• $\green\bigstar$ Area of Rectangle
• $\green\bigstar$ Perimeter of Rectangle

$\begin{gathered} \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Using Formulae:}}}}}}}\end{gathered}$

$\quad \dag{\underline{\boxed{\sf{{Breadth}^{2} = \big\{{Diagonal}^{2} - {Length}^{2}}\big\}}}}$

$\quad \dag\underline{\boxed{\sf{Area \: of \: Rectangle = Length × Breadth }}}$

$\quad \dag\underline{\boxed{\sf{Perimeter \: of \: Rectangle = 2(Lenght + Breadth)}}}$

$\begin{gathered} \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Solution:}}}}}}}\end{gathered}$

$\dag \: {\underline{\underline{\frak{\green{Firstly \: finding \: the \: Breadth \: of \: Rectangle..}}}}}$

$\quad {: \implies{\sf{{(Breadth)}^{2} = \bf\big\{{Diagonal}^{2} - {Length}^{2}}\big\}}}$

• Substituting the values

$\quad {: \implies{\sf{{(Breadth)}^{2}= \bf\big\{{145}^{2} - {143}^{2}}\big\}}}$

$\quad {: \implies{\sf{{(Breadth)}^{2} = \bf\big\{{(145 \times 145)} - {(143 \times 143)}}\big\}}}$

$\quad {: \implies{\sf{{(Breadth)}^{2}= \bf\big\{{21025} - {20449}}\big\}}}$

$\quad {: \implies{\sf{(Breadth)}^{2}= \bf{576}}}$

$\quad {: \implies{\sf{(Breadth)}= \bf{ \sqrt{576 }}}}$

$\quad {: \implies{\sf{(Breadth)}= \bf{ \sqrt{24 \times 24}}}}$

$\quad {: \implies{\sf{(Breadth)}= \bf{24 \: m}}}$

$\quad \dag{\underline{\boxed{\sf{Breadth}= \bf{24 \: m}}}}$

• Hence, The Breadth of Rectangle is 24 m.

$\begin{gathered} \end{gathered}$

$\dag \: {\underline{\underline{\frak{\green{Finding \: the \: Area \: of \: Rectangle..}}}}}$

$\quad {: \implies{\sf{Area \: of \: Rectangle = \bf{ Length × Breadth }}}}$

• Substituting the values

$\quad {: \implies{\sf{Area \: of \: Rectangle = \bf{ 143 × 24 }}}}$

$\quad {: \implies{\sf{Area \: of \: Rectangle = \bf{3432 \: {m}^{2} }}}}$

$\quad \dag\underline{\boxed{\sf{Area \: of \: Rectangle = \bf{3432 \: {m}^{2} }}}}$

• Henceforth,The Area of Rectangle is 3432 m².

$\begin{gathered} \end{gathered}$

$\dag \: {\underline{\underline{\frak{\green{Finding \: the \: Perimeter \: of \: Rectangle..}}}}}$

$\quad{ : \implies{\sf{Perimeter \: of \: Rectangle = \bf{ 2(Lenght + Breadth)}}}}$

• Substituting the values

$\quad{ : \implies{\sf{Perimeter \: of \: Rectangle = \bf{ 2(143 + 24)}}}}$

$\quad{ : \implies{\sf{Perimeter \: of \: Rectangle = \bf{ 2(167)}}}}$

$\quad{ : \implies{\sf{Perimeter \: of \: Rectangle = \bf{ 2 \times 167}}}}$

$\quad{ : \implies{\sf{Perimeter \: of \: Rectangle = \bf{334 \: m}}}}$

$\quad \dag{\underline{\boxed{\sf{Perimeter \: of \: Rectangle = \bf{334 \: m}}}}}$

• Henceforth,The Perimeter of Rectangle is 334 m.

$\begin{gathered} \end{gathered}$

$\dag \: {\underline{\underline{\frak{\green{Answer..}}}}}$

• Area of Rectangle = 3432 m²
• Perimeter of Rectangle = 334 m

$\begin{gathered} \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Diagram:}}}}}}}\end{gathered}$

$\begin{gathered}\begin{gathered}\tiny\begin{gathered} {\begin{gathered} \sf{24 \:m}\huge\boxed{ \begin{array}{cc} \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{143 \: m} \end{gathered}}\end{gathered}\end{gathered}\end{gathered}$

• Diagram of Rectangle.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 143 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 24 m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

• See the diagram from website Brainly.in..

$\begin{gathered} \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{purple}{Learn More:}}}}}}}\end{gathered}$

$\dag \: {\underline{\underline{\frak{\green{Properties\: of \: rectangle..}}}}}$

• Opposite sides of rectangle are parallel and equal to each other
• Each interior angle of rectangle is 90°
• The diagonals of rectangle bisect each other
• Both the diagonals of rectangle have the same length