Question

Find the perimeter of a rectangle whose width is 5 cm and diagonal is 13 cm.​

Answer 1

To find : perimeter of square  

Given : width = $5\ cm$ , diagonal = $13\ cm$

Solution :

• As per the given data we are given that , width and diagonal of rectangle are $5cm$ and $13\ cm$  respectively .
• As we know that , square of diagonal in a rectangle = $(length)^{2} + (width)^{2}$
• To find length , we substitute value in above formula ,

          $(13)^{2} = (l)^{2} + (5)^{2} \\(l)^{2} = 169 - 25\\(l)^{2} = 144 \\l = 12$  

• Now , to find perimeter we use formula ,

       Perimeter of rectangle = $2 ( l + b)$  

                                              $= 2 ( 12 + 5 ) \\= 2 \times 17 \\= 34 \ cm$

Hence , perimeter of rectangle will be $34 \ cm$ .

Answer 2

As per the data given in the question,

In the above question, it is given that,

The perimeter of a rectangle is 5cm

and the diagonal of a rectangle is 13cm

 Here we have to find the perimeter of a rectangle.

We have to use the formula of the perimeter.

The diagonal of the rectangle is $=(\text { length })^{2}+(\text { width })^{2}$

$\begin{array}{l}(13)^{2}=(l)^{2}+(5)^{2} \\(l)^{2}=169-25 \\(l)^{2}=144 \\l=12\end{array}$

Thus the perimeter is,

$\begin{array}{l}=2(l+b) \\=2(12+5) \\=2 \times 17 \\=34 \mathrm{~cm}\end{array}$

Hence the perimeter of the rectangle is 34cm.