Respuesta :
Answer:
The perimeter of the garden is 400 feet.
Step-by-step explanation:
Consider the provided information,
Raja is laying tiles on a path that forms the diagonal of a square garden. If Raja is told that the length of the diagonal path is [tex]100\sqrt{2}[/tex]
The length of the diagonal of a square garden is [tex]100\sqrt{2}[/tex]
Let x represent the side of square.
By Pythagorean theorem we know: [tex]a^2+b^2=c^2[/tex]
Where c is hypotenuse.
The diagonal of the square divides the square into two right angle triangle.
Where, the sides of the square are the legs of the triangle and diagonal is the hypotenuse of the triangle.
[tex]x^2+x^2=(100\sqrt{2})^2[/tex]
[tex]2x^2=(100\sqrt{2})^2[/tex]
[tex]x=100[/tex]
Hence, the side of the square is 100 ft.
The perimeter of the square is [tex]4s[/tex] where s is the side of square.
[tex]4(100)=400[/tex]
Hence, the perimeter of the garden is 400 feet.
