Greatest distance between a vertex of the inner square and a vertex of the outer square is 4cm
What is a Square?
Square: Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees
Perimeter of square₁, s₁=20
side of the square, a₁
4a₁=20
a₁=5
Perimeter of square₂, s₂=28
side of square, a₂
4a₂=28
a₂=7
So, a square with side 5 is inscribed in the square of side 7
By Pythagoras Theorem a² +b²=25 and a +b=7 (check the image)
we know that (a−b)²=2(a²+b²)−(a+ b)²
(a−b)²=2(25)-(7)²
(a−b)²=50-49=1
(a−b) =1 and a +b=7
a- b=1
a=1+b
substitute in a+ b=7
(1+b)+b=7
1+ 2b=7
2b=7-1
2b=6
b=3 and a=1+b=4
a=4cm and b=3cm is the distance of vertex of inner square to the vertex of outer square
Greatest distance between a vertex of the inner square and a vertex of the outer square is 4cm
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