★ Given :-
- The diagonal of the square is 7 cm
★ To Find :-
- The side and perimeter of the square.
★ Diagram :-
[tex] \boxed{ \red{Solution:-}}[/tex]
➳Let the side of the square be x cm.
➳Now, we know, each sides of square is of equal length.
➳Now, let the square be ABCD ( according to the attachment)
➳Therefore, AB = BC = CD = DA = x cm
➳The diagonal has divided the square into two triangles.
➳Now the each angles of a square is of 90°
➳Therefore, ∠DCB = 90°
➳And △DBC is a right angle triangle.
[tex] \boxed{ \sf{Hypotenuse^{2} = Base^{2} + height ^{2} }}[/tex]
[tex] \implies \sf \: {7}^{2} = {x}^{2} + {x}^{2} [/tex]
[tex] \implies \sf \: {7}^{2} = 2 {x}^{2} [/tex]
[tex] \implies \sf \: {x}^{2} = \dfrac{49}{2} [/tex]
[tex] \implies \sf \: {x}^{2} = 24.5[/tex]
[tex] \implies \sf \: x = \sqrt{24.5} [/tex]
[tex]\implies \boxed{ \red{\sf \: x = 4.95 }}[/tex]
➳ Therefore, the side of the square = 4.95 cm
Now, the perimeter = 4 × side
[tex] \sf \: Perimeter _{square} = 4 \times 4.95 [/tex]
[tex]\sf {\red{Perimeter _{square} = 19.8 }}[/tex]
➳ Therefore, the perimeter of the square is 19.8 cm^2
