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Why does rectangle fifty ft by thirty ft equal 1500 sq ft but a square forty ft by forty ft equals 1600 sq ft?
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
What else can I help you with?
What is equal parts of rectangle and square?
a square - an equilateral square a rectangle - an equilateral rectangle
Does a square and a rectangle has equal length?
A square (a by a) and a rectangle (a by b) can have sides that are of equal length.
Can a square also be a rectangle?
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.
Can a square be a rectangle?
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
When is a rectangle square?
A rectangle is a square when all four of its sides have equal length.
What is equal parts of rectangle and square?
a square - an equilateral square a rectangle - an equilateral rectangle
Does a square and a rectangle has equal length?
A square (a by a) and a rectangle (a by b) can have sides that are of equal length.
Is a rectangle a square or a square a rectangle?
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
Why is a square both a rectangle and a rhombus?
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.
Square and rectangle are the same or not?
A square is a rectangle however a rectangle is not a square because it doesn't have equal edges.
Why is a square a rectangle and a rectangle not a square?
A square is a rectangle, with the additional property of having four equal sides.
Is a square a rectangle and is a rectangle a square?
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
Can a square also be a rectangle?
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.
Can a square be a rectangle?
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
When is a rectangle square?
A rectangle is a square when all four of its sides have equal length.
Why is a a square a special rectangle?
A square is a rectangle whose adjacent sides are equal.
Why is the square is a special rectangle?
A square is a rectangle whose adjacent sides are equal.
