Question

A rectangular sheet of metal is 10 cm longer than it is wide. Squares 5 cm on a side, are cut from the corners of the sheet, and the flaps are bent up to form an open topped box having volume 6 liters. Find the original dimensions of the sheet of metal. 1L=1000cm³

Answer 1

let width be x
length = x+10
5cm is cut from the corners.
so length & width reduce by 10 cm.
..
the width will be x-10
length will be x+10-10
height will be 5cm
...
x(x-10)*5=6000 1 liter = 1000 cm^3
5x^2-50x-6000=0
/5
x^2-10x-600=0
x^2-30x+20x-600=0
x(x-30)+20(x-30)=0
(x-30)(x+20)=0
x= 30 the width
length = 40
...
CHECK
30*40*5= 6000 = 6 liters