The perimeter of the square is: [tex]20\sqrt2[/tex] ft
Step-by-step explanation:
The picture is attached with the answer.
the diagonal of a square divides it into two right angled-triangles.
We can use one of the triangle to find the length of side as the diagonal will be the hypotenuse of the triangle
Let a be the side of the square, then according to Pythagoras theorem
[tex]d^2=a^2+a^2\\(10)^2 = 2a^2\\2a^2=100[/tex]
Dividing both sides by 2
[tex]\frac{2a^2}{2}=\frac{100}{2}\\a^2=50[/tex]
Taking Square root on both sides
[tex]\sqrt{a^2}=\sqrt{50}\\a=\sqrt{25*2}\\a=\sqrt{5^2 * 2}\\a=5\sqrt{2}\ ft[/tex]
Now,
[tex]P = 4a\\P = 4 * 5\sqrt{2}\\=20\sqrt{2}\ ft[/tex]
Hence,
The perimeter of the square is: [tex]20\sqrt2[/tex] ft
Keywords: Perimeter, Pythagoras Theorem
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