Question

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open
box. If the volume of the box is 1050 in3, what were the original dimensions of the piece of metal?
What is the original width? in
What is the original length in

Answer 1

breadth= X

L= x+30

after you cut a square with 6in from the corners, the length becomes x+30-6 =x+24 and breadth becomes x-6.

The eqn for volume of box is Length x Breadth x height

it's given that LxBxH = 1050

here height is 6, because u are folding the edge where it's been cut off and that side becomes the height.

rewrite with the given information we get

(x+24)*(x-6)*6 = 1050

divide both sides with 6

(x+25)*(x-6) = 175

distribute the brackets we get,

x^2 -18x -144 =175

x^2 -18x-319 = 0

solve for x using quadratic formula.

we get x= 29, -11

since length cannot be negative x= 29

B= 29, L=59.