Question

A square and a rectangular plot of land have the same perimeter. If the square is of side $40m$ and the rectangle is of length $5$ decameter. Then area of rectangle is _______ .

• A. $1500m^2$
• B. $1600m^2$
• C. $200m^2$
• D. $150m^2$

Answer 1

The correct option is A $1500m^2$

$\Rightarrow$ Length of a rectangle $=5$ decameter $=50m$

$\Rightarrow$ Side of square = $40m$

$\therefore$ Perimeter of squares = $4\times 40=160m$

$\Rightarrow$ It is given that, perimeter of square = perimeter of a rectangle.

$\Rightarrow$ Perimeter of rectangle = $2(l+b)$

$\therefore$ $160=2(50+b)$

$\therefore$ $80=50+b$

$\therefore$ $b=30m$

$\Rightarrow$ Area of a rectangle $=l\times b=50\times 30=1500m^2$