Answer:
44 inches and 24 inches
Step-by-step explanation:
Let [tex]l,b[/tex] denotes length and breadth of a rectangle.
[tex]lb=1056[/tex]
A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides.
New length [tex]=l-6[/tex] inches
New breadth [tex]=b-6[/tex] inches
Height of box [tex]=3[/tex] inches
Volume of box = length × breadth × height
[tex](l-6)(b-6)3=2052[/tex]
[tex]lb-6l-6b+36=684\\6(l+b)=408\\l+b=68\\b=68-l[/tex]
Put [tex]b=68-l[/tex] in [tex]lb=1056[/tex]
[tex]l(68-l)=1056\\l^2-68l+1056=0\\l^2-44l-24l+1056=0\\l(l-44)-24(l-44)=0\\(l-24)(l-44)=0\\l=24,44[/tex]
At [tex]l=24,b=\frac{1056}{24}=44[/tex] inches
At [tex]l=44,b=\frac{1056}{44}=24[/tex] inches
