Length- Side of Box / Solution - Explanation

A metal box is to be made from a square piece of metal by removing 4 inch square pieces from the corners and turning up the sides. The box is 4 inches in height and contains 100 cubic inches.

Calculate length of side of metal used.

Solution included with problem:

D C
G F D , C , A, B are shaded.

H E
A B


AB = BC

Let l = length

HE = l in. - 2 x 4 = (l - 8) in. **

FE = ( l - 8) in. **

Bottom of box - (l - 8) sq. in. **

Height of box - 4 in.

Volume - ( l - 8) * ( l - 8 ) * 4 = 4 (l - 8)^2 cu. in. **

4 (l - 8 ) ^2 = 100

(l - 8) = 25

( l - 8) = 5 or - 5

(5) ^ 2 = 25 or (-5 ) ^2 = 25

l + 8 = 13 or l = - 3


** I don't understand these steps.