Answer :
Answer:
[tex]\displaystyle 48-2(3)=42\ inches[/tex]
[tex]\displaystyle 36-2(3)=30\ inches[/tex]
The height of the box is 3 inches
Step-by-step explanation:
A box has three perpendicular dimensions (a,b,c). Let's assume a and b are the dimensions of the base, and c is the height. The volume of the box is
[tex]\displaystyle V=a\ b\ c[/tex]
And the area of the base is
[tex]\displaystyle A=a\ b[/tex]
The rectangular sheet of copper has dimensions 48 inches and 36 inches. We are cutting out squares corners from each end.
Set x=side of each square corner. Those corners will be folded up, leaving a base of dimensions (36-2x) and (48-2x). Its area is
[tex]\displaystyle A=(36-2x)(48-2x)[/tex]
According to the conditions of the question that area must be 1260 square inches, so
[tex]\displaystyle (36-2x)(48-2x)=1260[/tex]
Operating
[tex]\displaystyle 1728-168x+4x^2=1260[/tex]
Rearranging
[tex]\displaystyle 4x^2-168x+468=0[/tex]
Dividing by 4
[tex]\displaystyle x^2-42x+117=0[/tex]
Factoring
[tex]\displaystyle (x-3)(x-39)=0[/tex]
We find two solutions
[tex]\displaystyle x=3\ ,\ x=39[/tex]
The solution x=39 is unfeasible because it will result in negative dimensions of the base of the box. We keep x=3 as the solution. The dimensions of the base are
[tex]\displaystyle 48-2(3)=42\ inches[/tex]
[tex]\displaystyle 36-2(3)=30\ inches[/tex]
And the height of the box is x=3