Question

Find the length of the diagonal of a rectangle of the length 30 meter and width 16 meter.​

Answer 1

${\boxed{ \LARGE{ \purple{ \rm{ \underline{ Given}}}}}}$

• Length of rectangle = 30 meter.

$\:$

• Width of rectangle = 16 meter.

_________________________

${\boxed{ \LARGE{ \purple{ \rm{ \underline{ To \: \: Find}}}}}}$

• Diagonal of a rectangle.

_________________________

${\boxed{ \LARGE{ \purple{ \rm{ \underline{ Formula \: \: Using}}}}}}$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\red{ \: D \: = \: \sqrt{ {W }^{2} \: + \: {L} ^{2} } }}}}}\end{gathered}$

• D denotes the diagonal of rectangle.

$\:$

• W denotes width of rectangle.

$\:$

• L denotes length of rectangle.

_______________________

$\Large \pink\dag \: \underline {\rm {{{\color{blue}{Substuting \: \: the \: \: values...}}}}} \: \pink\dag$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\green{ \: D \: = \: \sqrt{ {16 }^{2} \: + \: {30} ^{2} } }}}}}\end{gathered}$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\green{ \: D \: = \: \sqrt{ 256\: + \: 900 } }}}}}\end{gathered}$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\green{ \: D \: = \: \sqrt{1156} }}}}}\end{gathered}$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\green{ \: D \: = \: \sqrt{2 \: \times \: 2 \: \times \: 17 \: \times \: 17} }}}}}\end{gathered}$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\green{ \: D \: = \: {2 \: \times \: 17} }}}}}\end{gathered}$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\green{ \: D \: = \: 34 }}}}}\end{gathered}$

⇨ Length of the Diagonal of rectangle is 34 m.

$\:$

☛ More Information.

$\:$

Area of rectangle = Length × Breadth

$\:$

Perimeter of rectangle = 2 ( L + B ).

Answer 2

Answer:

$\underline{\underline{\bigstar{\textbf{\textsf{\: Given\::-}}}}}$

• ➽ Lenght of Rectangle = 30 meter
• ➽ Width of Rectangle = 16 meter

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

$\underline{\underline{\bigstar{\textbf{\textsf{\: To Find \::-}}}}}$

• ➽ Diagonal of Rectangle

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

$\underline{\underline{\bigstar{\textbf{\textsf{\: Using Formula\::-}}}}}$

$\dag{\underline{\boxed{\pmb{\sf{\red{{D} = \sqrt{ {l}^{2} + {w}^{2}}}}}}}}$

Where

• ➽ D = Diagonal of Rectangle
• ➽ L = Lenght of Rectangle
• ➽ W = Width of Rectangle

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

$\underline{\underline{\bigstar{\textbf{\textsf{\: Diagram\::-}}}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large{30 cm}}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large{16 cm}}\put(-0.5,-0.4){\bf}\put(-0.5,3.2){\bf}\put(5.3,-0.4){\bf}\put(5.3,3.2){\bf}\end{picture}$

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• Here is the question link :
• https://brainly.in/question/43495813

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

$\underline{\underline{\bigstar{\textbf{\textsf{\: Solution\::-}}}}}$

Finding the Diagonal of Rectangle

$\quad{: \implies{\sf{{D} = \sqrt{ {l}^{2} + {w}^{2}}}}}$

• Substuting the values

$\quad{: \implies{\sf{{D} = \sqrt{ {(30)}^{2} + {( 16 )}^{2}}}}}$

$\quad{: \implies{\sf{{D} = \sqrt{ {(30 \times 30)} + {( 16 \times 16 )}}}}}$

$\quad{: \implies{\sf{{D} = \sqrt{ {900} + {256}}}}}$

$\quad{: \implies{\sf{{D} = \sqrt{1156}}}}$

$\quad{: \implies{\sf{{D} = \sqrt{34 \times 34}}}}$

$\quad{: \implies{\sf{{D} = {34 \: m}}}}$

$\dag{\underline{\boxed{\pmb{\sf{\red{Diagonal \: of \: Rectangle = 34 \: m}}}}}}$

∴ The Diagonal of Rectangle is 34 m.

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

$\underline{\underline{\bigstar{\textbf{\textsf{\: Learn More \::-}}}}}$

$\small\boxed{\begin{minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star\sf Scalene\triangle=\sqrt{s (s-a)(s-b)(s-c)}\\ \\ \star\sf Rhombus =\dfrac{1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac{1}{2}p\sqrt{4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac{1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac{\sqrt{3}}{4}(side)^2\end{minipage}}$

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