Question

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Find the perimeter of the rectangle with diagonal 13cm and length of one side is 12cm ​

Answer 1

$\textbf{\large{\underline{Answer :-}}}$


The Perimeter of the Rectangle is 34 cm

$\textbf{\large{\underline{Explaination :-}}}$


$\textbf{\large{\underline{Given :-}}}$


Diagonal = 13 cm

Length of one side = 12cm

$\textbf{\large{\underline{To find :-}}}$


The Perimeter of the Rectangle

$\textbf{\large{\underline{Solution :- }}}$


To find the Perimeter, we need to find the Breadth.

Refer the Attachment for the diagram.

Let ABCD reperesent the given Rectangle with diagonal BD = 13cm

We know each Angle of a Rectangle is 90°

$\mathsf{\rightarrow \angle \: C = 90\degree}$

$\mathsf{\rightarrow In, \triangle \: BDC, BD \: is \: the \: Hypotenuse}$

$\mathsf{\rightarrow By \: pythagoras \: theorum}$

$\mathsf{\Rightarrow BD^{2} = DC^{2} + BC ^{2} }$

$\mathsf{\Rightarrow 13^{2} = 12 ^{2} + BC^{2} }$

$\mathsf{\Rightarrow 169 = 144 + BC^{2} }$

$\mathsf{\Rightarrow169 - 144 = BC^{2} }$

$\mathsf{\Rightarrow 25 = BC ^{2} }$

$\mathsf{\Rightarrow \: BC = \sqrt{25} }$

Square root of 25 =

$\begin{array}{r|l}5& 25 \\\cline{1-2} 5 & 5 \\\cline{1-2} & 1\end{array}$

25 = 5 × 5

$\textbf{Square root = 5}$


$\mathsf{\Rightarrow \: BC \: = 5 }$

Thus the Length of the other side 5cm

Now, the Perimeter of Rectangle =

$\mathsf{\Rightarrow2(l + b) }$

$\mathsf{\Rightarrow 2(12 + 5)}$

$\mathsf{\Rightarrow24 + 10 }$

$\mathsf{\Rightarrow 34}$

$\therefore$The Perimeter of the Rectangle is 34 cm