Question

diagonal of a square is 25√2 find perimeter of square​

Answer 1

If the diagonal of a square is 25√2 then,

The side of the square will be

$\frac{ 25\sqrt{2} }{ \sqrt{2} }$

=25

Now,

The perimeter of the square

= 4L

= 4×25

=100

^-^

Answer 2

$\bf{ \underline{ \underline{Answer \: : }}} \\ \\ \large\bold\red{Answer~is \: 100 \: cm \: .}$

$\mathrm{⟹ \: we \:know \: that \: square \: have} \\ \mathrm{ \: \: \: \: \: \: \: \: \: \: all \: angles \: of \: 90°} \: \\ \\ \mathrm{⟹ \: diagonal \: of \: square \: is \: hypotenus} \\ \\ ⟹ \: \mathrm{ In~right~triangle, \: } \\ \\⟹ \: \mathrm {(Hypotenus)}^{2} = \mathrm{sum \: of \:squares \: of \: two \: sides}$

$\\ \mathrm{⟹we \: know \: that \: square \: have \: all} \\ \mathrm { \: \: \: \: \: \: \: \: equal \: sides \: .} \\ \\ \mathrm ⟹ {(Hypotenus)}^{2} = 2 {( \mathrm{side})}^{2} \:$

$⟹ {(25 \sqrt{2}) }^{2} = 2 {(side)}^{2} \\ \\ ⟹ 1250 = 2 {(side)}^{2} \\ \\ ⟹ \frac{1250}{2} = {(side)}^{2} \\ \\ ⟹ 625 = {(side)}^{2} \\ \\ ⟹ side = \sqrt{625} \\ \\ ⟹ side = 25 \: cm$

$\\ \\ \\ ⟹ \mathrm{Perimeter \: } \: = 4 \times \mathrm{side} \\ \\ ⟹\mathrm{Perimeter \: } = \: 4 \times 25 \\ \\ ⟹ \mathrm{Perimeter \: } \: = 100 \: cm$

$\small\bold\orange{Answer~is \: 100 \: cm \: .}$