Prove that area of rectangle is length into breadth
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Theorem: The area of a rectangle is the product of its length and width.
Consider the square below with side length units. The square is divided into four parts: two squares and two rectangles. We already know that the area of the two squares are and . We do not know the area of the rectangle yet because that is what we are trying to prove.
Now, let be the area of each rectangle shown above. Clearly, the area of the largest square is the sum of the areas of the two smaller squares and the two rectangles. In equation form, we have
(x+y)(x+y)
=x2+y2+2x
Expanding the left hand side, we have
x2+2xy+y2=x2+ye+2x
Subtracting x^2 + y^2 from both sides results to
2xy=2a
Solving for gives us
.a=xy
But and are the length and width of the rectangle, therefore, the area of any rectangle is the product of its length and its width.
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