♕ Answer
The length of the side is 40.
Solution:
We know that
- the perimeter P of a square is four times the length of the side, and
- the area A of a square is the square of its sides.
Given that the area of a square is ten times its perimeter, we find the length of the side by solving for s,
- [tex]{\tt{A=10(P)}}[/tex]
- [tex]{\tt{s^{2}=10(4s)}}[/tex]
- [tex]{\tt{s^{2}=40s}}[/tex]
- [tex]{\tt{{\frac{s^{2}}{s}}={\frac{40s}{s}}}}[/tex]
- [tex]{\boxed{\green{\tt{s=40}}}}[/tex]
To check:
- [tex]{\tt{A=10(P)}}[/tex]
- [tex]{\tt{s^{2}=10(4s)}}[/tex]
- [tex]{\tt{s^{2}=40s}}[/tex]
- [tex]{\tt{(40)^{2}=40(40)}}[/tex]
- [tex]{\underline{\tt{1,600=1,600}}}[/tex]
❤︎Tsareena♕
[tex]{\huge{\underline{\sf{Hope\:It\:Helps}}}}[/tex]
#CarryOnLearning
