Question

The length of a rectangular piece of land is 15m and it's 8m. Find the length of its diagonal?​

Answer 1

$\star \; {\underline{\boxed{\pmb{\orange{\sf{ \; Given \; :- }}}}}}$

• Length of Rectangle = 15 m
• Breadth of Rectangle = 8 m

$\star \; {\underline{\boxed{\pmb{\color{darkblue}{\sf{ \; To \; Find \; :- }}}}}}$

• Diagonal of Rectangle = ?

$\\ \qquad{\rule{200pt}{2pt}}$

$\star \; {\underline{\boxed{\pmb{\red{\sf{ \; SolutioN \; :- }}}}}}$

$\; \dag \; {\pmb {\underline{\underline{\sf{ \: Formula \; Used \; :- }}}}}$

$\qquad \; \; {\green{\bigstar \; \; {\purple{\underbrace{\underline{\pink{\sf{ {Diagonal}^{2} = {Length}^{2} + {Breadth}^{2} }}}}}}}}$

$\; \dag \; {\pmb {\underline{\underline{\sf{ \: Calculation \; :- }}}}}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { {Diagonal}^{2} = {Length}^{2} + {Breadth}^{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Diagonal = \sqrt{ { \bigg( Length \bigg) }^{2} + { \bigg( Breadth \bigg)}^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Diagonal = \sqrt{ { \bigg( 15 \bigg) }^{2} + { \bigg( 8 \bigg)}^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Diagonal = \sqrt{ 225 + 64 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Diagonal = \sqrt{ 289 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\purple{\pmb{\sf { Diagonal = 17 \; cm }}}}}} \; \red\bigstar \\\ \\ \\ \end{gathered}$

$\therefore \;$ Diagonal of the Rectangle is 17 cm .

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Answer 2

$\sf \bigstar \underline{\: Information \: provided \: with \: us :}$

⭐ The length of rectangular piece of land is

• ➡ 15 m

⭐ The breadth of rectangular piece of land is

• ➡ 8 m

$\sf \bigstar \underline{ \: What \: we \: have \: to \: calculate :}$

• ⭐ ➡ The length of its diagonal

$\sf \bigstar \underline{ \: Assumption :}$

➡ Let ABCD is rectangular piece of land of given length and breadth .Since ABCD is right angle triangle So we know that each angle of reactangle is 90 °

➡ Consider the diagonal be d m

$\sf \bigstar \underline{ \: Formula \: used :}$

➡ The formula to calculate length of diagonals of a rectangle are as follows,

$\rm \implies \: d = \sqrt{ {l}^{2} + {w}^{2} }$

where,

• l = length of the rectangle

• w = width of the rectangle

$\sf \bigstar \underline{ \: Now :}$

⭐ Note :-

➡ d = diagonal = AC = ?

➡ l = length = BC = 15 m

➡w = width = AB = 8 m

⭐ Therefore by using Pythagoras theorem

$\rm \implies \: {d}^{2} = {l}^{2} + {w}^{2}$

$\rm \implies \: A {C}^{2} = B {C}^{2} + A {B}^{2}$

➡ Now by Taking square root on both sides,

$\rm \implies \: AC = \sqrt{ {l}^{2} + {w}^{2} }$

$\rm \implies \: AC = \sqrt{B {C}^{2} + A {B}^{2}}$

➡ Here by substituting the given values in above diagonal of a rectangle formula we get :-

$\rm \implies \: AC = \sqrt{ {15}^{2} + {8}^{2} }$

$\rm \implies \: AC= \sqrt{ 225 + 64}$

$\rm \implies \: AC = \sqrt{ 289 }$

$\rm \implies \: AC= 17 \: m$

$\sf \bigstar \underline{ \: Therefore :}$

⭐ The length of diagonal

• ➡ AC = 17 m