Question

If the length of diagonals of a rhombus FOUR is 18 cm and 24 cm respectively, then find the perimeter of FOUR.Please help

Answer 1

$\huge{ \bold{ \underline {\underline{Given:}}}}$

$\bold{Lengths \: of \: diagonals \: of \: rhombus} \\ \bold{is \: 18cm \: and \: 24cm \: respectively}$

$\huge{ \bold{ \underline {\underline{To \: find:}}}}$

$\bold{Perimeter \: of \: rhombus} \\ \bold{perimeter = 4(side)}$

${ \bold{ \underline {\underline{Step-by-step \: explanation :}}}}$

$\bold{Half \: of \: the \: diagonals=9cm,24cm}$

$\bold{ \underline{ \underline{By \: pythogorous \: theorem:}}}$

$\bold{ {hypotunues}^{2} = {side}^{2} + {side}^{2} } \\ \bold{ \: \: \: \: \: \: \: \: {hyp }^{2} = {9}^{2} + {12}^{2} } \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: hyp = \sqrt{81 + 144} } \\ \bold{hyp = \sqrt{225} } \\ {\bold{ \boxed{hyp =15cm }}}$

We know that ,

Hypotenuse is the side of rhombus i.e, 15cm.

Perimeter of Rhombus = 4(side)

= 4(15)

= 60cm

Therefore,

Perimeter of Rhombus is

$\huge \boxed{ \fcolorbox{pink}{yellow}{60cm}}$

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