[tex]\bold{\huge{\underline{ Solutions }}}[/tex]
Given :-
- The length of a diagonal is 20 cm
To Find and prove :
- We have to find the length of a side of the square
- We also have to show that the area of square is 200 cm²
Solution ( a)
We have,
- The length of the diagonal of a square is 20 cm
We know that,
[tex]\bold{\red{ d = }}{\bold{\red{\sqrt{2}}}}{\bold{\red{ a }}}[/tex]
- Where, a is the length of the side of the square
- d is the the length of the diagonal
Subsitute the required values in the above formula :-
[tex]\sf{ 20 = }{\sf{\sqrt{2}}}{\sf{ a }}[/tex]
Squaring on both the sides :-
[tex]\sf{ 400 = 2a^{2}}[/tex]
[tex]\sf{\dfrac{400}{2}}{\sf{ = a^{2}}}[/tex]
[tex]\sf{ 200 = a^{2}}[/tex]
[tex]\bold{ a = 14.14 cm }[/tex]
Hence, The side of the square is 14.14 cm
Solution ( b) :-
Here, we have to prove that,
- The area of square is 200 cm²
We know that,
Area of square
[tex]\bold{\pink{ = side}}{\bold{\pink{\times{ side}}}}[/tex]
- The side of the square is 14.14 cm
Subsitute the required values,
[tex]\sf{ = 14.14 }{\sf{\times{ 14.14}}}[/tex]
[tex]\bold{ = 200 cm^{2}}[/tex]
Hence, It is proved that the area of the square is 200 cm².
