What happens to the area of a rectangle if its length as well as its breadth is doubled ?

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Solution

Step 1:
Area of rectangle $= l e n g t h \times b r e a d t h$
Let initial length be $x u n i t$ and breadth $y u n i t$
Initial area $= x y s q u a r e u n i t$
Step 2:
New length when doubled is $2 x u n i t$ and new breadth when doubled $2 y u n i t$ .
New area $= 2 x \times 2 y = 4 x y s q u a r e u n i t$ [Area of rectangle $= l e n g t h \times b r e a d t h$ ]
Step 3:
Impact on area of rectangle $= \frac{N e w a r e a}{I n i t i a l a r e a} = \frac{4 x y}{x y} = 4 t i m e s$
Hence, area of rectangle become $4 t i m e s$ when length is doubled and breadth is doubled..

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