Question

A rectangle whose area is $180m^2$has its sides respectively diminished by $7m$ and $4m$ so as to form a square. Find the side of the square.

Answer 1

Let the side of the rectangle be $x$ and $y$

Area of the rectangle $=length\times breadth$

$\therefore xy=180$ [$\because$ Area of rectangle $=180m^2$ (given) ]
$\Rightarrow x=\frac{180}{y}$

When the dimension of the given rectangle will be diminished by $7m$ and $4m,$ then it will become square.

Length will be reduced by $7m,$ then side of square $=x-7m$

and, breadth will be reduced by $4m$, then side of square $=y-4m$

We know that the sides of a square are equal.

$x-7=y-4$

$\Rightarrow x-y=3$

$\Rightarrow \frac{180}{y}-y=3$

$\Rightarrow y^2+3y-180=0$

$\Rightarrow y^2+15y-12y-180=0$

$\Rightarrow y(y+15)-12(y+15)=0$

$\Rightarrow (y-12)(y+15)=0$

$\Rightarrow y=12$ [$\because$ Length cannot be negative, $y\ne$ negative]

$\therefore x=12+3=15$

So, sides of the square $=y-5=12-4=8m$