Question

The longest rod that can be placed flat on the bottom of a box is $45cm$. The box is $9cm$ longer than it is wide. Find the length and breadth of the box.

Answer 1

Let the length of the rod be $=x+9$cm

Let the width of the rod$=x$xm

The diagonal$=45$cm

$x^2+(x+9{)}^2={45}^o$

$2x^2+18x-1944=0$

$x^2+9x-972=0$

$(x+36)(x-27)=0$

$x=27$

length$=36$cm.