Question

prove that area of rectangle length ×breadth

Answer 1

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.

Answer 2

Here is your answer



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Draw the diagonals of a rectangle It will divide the rectangle into two right angle triangle
(Diagonals of rectangle are equal )


Area of right angle triangle 1/2× l×b



There are 2 such triangles


Therefore A=2 (l+b)






Hope it help you





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