Question

Balvinder father had a rhombus shaped plot with diagonals of 20 and 40 metres long . he sold the plot of same area. find the perimeter of new plot​

Answer 1

────────────────────────────────

❑ ƛƝꜱƜЄƦ

$\small \red{Given}$

$\small\red{{First \: diagonal \: of \: the \: rhombus \: = 20 m}}$

$\small \red{{ second \: of \: the \: rhombus = \: 40 m}}$

$\small\red{{We \: know \: that ,}}$

$\small \red{Area \: of \: a \: rhombus = \: \frac{1}{2} \times d(1) \times d(2)}$

$\small \red{{\tt \implies \: \frac{1}{2} \times 20 \times 40 }}$

$\small \red{{ \tt \implies \: \frac{1}{2} \times 800 }}$

$\small \red{{\tt \implies \frac{1}{2} \times 800 = 400 \: m^{2} }}$

$\small \red{{And \: also \: given \: that ,}}$

$\small \red{{Area \: of \: the \: rhombus \: = Area \: of \: square}}$

$\small \red{{We \: know \: that \: , area \: of \: a \: square = (Side)^{2} }}$

$\small \red{{Hence , \: 400 \: m^{2} = (side)^{2} }}$

$\small \red{{ \tt \implies \:(20)^{2} =(side)^{2} }}$

$\small\red{{ \tt \implies \:side = \sqrt{(20)^{2} }}}$

$\small \red{{\tt\implies \:Side = 20 \: m}}$

$\small \red{{We \: know \: that , \: Perimeter \: of \: a \: square = \: 4 \times Side}}$

$\small \red{{\tt \implies \: 4 \times 20 \: m}}$

$\small \red{{ \tt \implies \: 80 \: m}}$

$\small \red{{Hence \: , Perimeter \: of \: a \: square \: = 80 m }}$

────────────────────────────────