Explaining why will take a little bit of algebra:
Take any two numbers a and b. Calculate the average and call it x. So x = (a+b)/2 = a/2+b/2
Now x+a/2-b/2 = a/2+b/2+a/2-b/2 = a
and x-a/2+b/2 = a/2+b/2-a/2+b/2 = b.
So, if you write c for a/2-b/2, then
a=x+c and b = x-c.
Now, a*b = (x+c)*(x-c) = x2-xc+xc-c2 = x2-c2
But c2 is always non-negative (zero or positive) so x2-c2 is always less than x2. It reaches its maximum value when c2 = 0 which is when c = 0 or when a = x = b.
In your example, a = 30, b = 50, x = 40 and c = 10
a square - an equilateral square a rectangle - an equilateral rectangle
A square (a by a) and a rectangle (a by b) can have sides that are of equal length.
A square is a special case of a rectangle. Every square is a rectangle, but not every rectangle is a square. A square is a rectangle with four sides that are all equal in length.
No. A square by definition is a shape with 4 "equal" sides yes a square is a rectangle because a rectangle has everything but equal sides so it is still the same
A rectangle is a square when all four of its sides have equal length.
a square - an equilateral square a rectangle - an equilateral rectangle
A square (a by a) and a rectangle (a by b) can have sides that are of equal length.
A square is rectangle with all its sides are equal in length. The rectangle has: (a) opposites sides are parallel. (b) opposite angles are equal
A rectangle is an oblong, as its sides are not equal. A square has equal sides. Therefore, a square is not a rectangle. A rhombus is a parallelogram with oblique angles and equal sides.
A square is a rectangle however a rectangle is not a square because it doesn't have equal edges.
A square is a rectangle, with the additional property of having four equal sides.
A square is a rectangle, but a rectangle isn't necessarily a square. A square can be thought of as a "special" rectangle, where all sides are equal. The similarity is that all rectangles have 4 angles each of 90o However a Square has 4 sides equal length while a Rectangle has 4 sides with opposite sides of equal length. The clever observer will note that the adjacent sides of a square are equal while the adjacent sides of a rectangle may or may not be equal. yes it is
A rectangle is a plane four sided shape. It has two pairs of parallel sides which meet at right angles. So is a square. The opposite sides of a rectangle are equal but in a square all four sides are equal. So a square is a rectangle but a rectangle is not a square.
A square is a special case of a rectangle. Every square is a rectangle, but not every rectangle is a square. A square is a rectangle with four sides that are all equal in length.
No. A square by definition is a shape with 4 "equal" sides yes a square is a rectangle because a rectangle has everything but equal sides so it is still the same
A square is a rectangle whose adjacent sides are equal.
A rectangle is a square when all four of its sides have equal length.