LENGTH[tex]=======================[/tex]
[tex]{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\[/tex]
[tex] \large \qquad\qquad\boxed{ \sf{ \: \bold{ \:Length = 17 \: units} \: }} \\[/tex]
[tex]=======================[/tex]
[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}} \\[/tex]
[tex] \sf{Given:}[/tex]
- The area of square board is 289 sq. units.
[tex] \sf{To \: find:}[/tex]
- Length of the side of square board.
Given that, the area of square board is 289 sq. units.
Let assume that length of side of square board = x units.
We know,
[tex] \quad\qquad \hookrightarrow \: \boxed{ \bold{ \:Area_{(Square)} = {(side)}^{2} \: }} \\ [/tex]
[tex] \large \sf{So,}[/tex]
[tex]\sf \qquad\quad\implies \: 289 = {x}^{2} \\[/tex]
[tex]\sf \qquad\quad\implies \: \sf \: {x}^{2} = 289 \\[/tex]
[tex]\sf \qquad\quad\implies \: \sf \: {x}^{2} = 17 \times 17 \\[/tex]
[tex]\sf \qquad\quad\implies \: \sf \: {x}^{2} = {(17)}^{2} \\[/tex]
[tex]\sf\qquad\quad \implies \: \bold{ \:x = 17 \: units} \\ [/tex]
Hence,
[tex]\sf\implies \bold{ \:Length\:of\:side = } \underline{ \bold{ \pmb{ \: \: 17 \: units \: \: }}} \\[/tex]
[tex]=======================[/tex]