Answer = 55,25 inches
Solution -
let's take x as length and y as width of the metal piece. As per the question x is 30 more than y,
⇒ x = y + 30
Then four square pieces of side 6 are cut from each corner,
so the new length and width are
x-12 , y-12
Then the volume of the new box created will be
(x-12)(y-12)6
in the question the volume of the given figure is given to be 3354
so (x-12)(y-12)6 = 3354
putting the value of x in the the above equation
⇒ (y+30 - 12)(x-12) = 3354/6 = 559
⇒ (y+18)(y-12) = 559
⇒ y² + 6y - 775 = 0
⇒ y² + 31y - 25y -775 = 0
⇒ (y+31)(y-25) = 0
⇒ y = -31, 25
as length can not be -ve , so y = 25
then x = 25+30 = 55
Hence the dimensions of the metal piece are 55, 25 inches
