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an open box is to be constructed from a rectangular piece of cardboard by removing a square of size 2 inches from each corner and turning up the edges. the box is to hold 56 cubic inches and the length of the piece of cardboard is 3 times its width. find the dimensions of the piece of cardboard Solution Let \'L\' be the length of the card board and \'B\' be the breadth of it in inches from the data, the length of an open box =L-4 and breadth of open box=B-4 the height of the box=2 inches then, the volume of the box is given that, V=56 cubic inches the volume of the box when it is done as in the problem V=2(L-4)(B-4) so, 2(L-4)(B-4)=56 LB-4L-4B+16=28 LB-4(L+B)=12 but, according to the data, L=3B 3B 2 -4(3B+B)=12 3B 2 -16B-12=0 3B 2 -18B+2B-12=0 3B(B-6)+2(B-6)=0 (B-6)(3B+2)=0 B-6=0 (or) 3B+2=0 B=6(or) B=(-2/3) so, B=6 inches L=3B=3*6=18 inches so, the length of the piece of the card board is,L=18 inches and breadth is,B=6 inches .

an open box is to be constructed from a rectangular piece of cardboard by removing a square of
size 2 inches from each corner and turning up the edges. the box is to hold 56 cubic inches and
the length of the piece of cardboard is 3 times its width. find the dimensions of the piece of
cardboard
Solution
Let 'L' be the length of the card board and
'B' be the breadth of it in inches
from the data,
the length of an open box =L-4
and breadth of open box=B-4
the height of the box=2 inches
then, the volume of the box is given that, V=56 cubic inches
the volume of the box when it is done as in the problem
V=2(L-4)(B-4)
so, 2(L-4)(B-4)=56
LB-4L-4B+16=28
LB-4(L+B)=12
but, according to the data, L=3B
3B 2
-4(3B+B)=12
3B 2
-16B-12=0
3B 2
-18B+2B-12=0
3B(B-6)+2(B-6)=0
(B-6)(3B+2)=0
B-6=0 (or) 3B+2=0
B=6(or) B=(-2/3)
so, B=6 inches

L=3B=3*6=18 inches
so, the length of the piece of the card board is,L=18 inches
and breadth is,B=6 inches

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2. L=3B=3*6=18 inches so, the length of the piece of the card board is,L=18 inches and breadth is,B=6 inches