question_answer

                        The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20% we get the same perimeter. Find the length and breadth of the rectangle.

Answer:

Let the length of rectangle be x

The breadth of a rectangle be b.

Perimeter of a rectangle = 2 (x + b)

2 (x + b) = Perimeter

2 (x + b) = 240

\[x+b=\frac{240}{2}\]

x+b=120

or,            \[b=120-x\]

New length = x + 10% of x

\[=x+\frac{10x}{100}=x+\frac{x}{10}\]

\[=\frac{11x}{10}\]

New breadth

\[=\left( 120-x \right)-20%\text{ }of\left( 120\text{ }-\text{ }x \right)\]

\[=(120-x)-\frac{20}{100}\times (120-x)\]

\[=120-x-\frac{1}{5}(120-x)\]

\[=120-x-\frac{120}{5}+\frac{x}{5}\]

\[=120-x-24+\frac{x}{5}\]

\[=96-x+\frac{x}{5}\]

\[=\frac{480-5x+x}{5}\]

\[=\frac{480-4x}{5}\]

According to condition,

or,   \[2\left( \frac{11x}{10}+\frac{480-4x}{5} \right)=240\]

or,\[\frac{11x}{10}+\frac{480-4x}{5}=120\]

\[\frac{11x+960-8x}{10}=120\]

\[\frac{3x+960}{10}=120\]

\[3x+960=1200\]

\[3x=1200-960\]

\[3x=240\]

\[x=\frac{240}{3}=80\]

Hence,

length = x = 80 cm

breadth \[=120-x=120-80=40\text{ }cm\]