Respuesta :
Answer:
The surface area of the box is [tex]1280 sq. inches[/tex].
Step-by-step explanation:
Given that,
Ratio of the length to the width to the height of a rectangular box is [tex]12:4:7.[/tex]
The sum of the length and width of box is [tex]32.[/tex]
From the question,
Dimension of Rectangular box are [tex]Length (l),\ Width (w) , Height (h)[/tex].
Let the side of rectangular box is x.
[tex]length = 12x\\\\width = 4x\\\\Height = 7x[/tex]
Now, Sum of length and width is [tex]32[/tex][tex]inches[/tex]
Then, [tex]12x+4x=32[/tex]
⇒ [tex]16x=32[/tex]
⇒ [tex]x=\frac{32}{2} = 2\\[/tex]
Here we get the dimensions are,
[tex]length = 12x=24inches\\width = 4x=8inches\\Height = 7x=14inches[/tex]
Then, surface Area of rectangular box = [tex]2(lw+wl+ hl)[/tex]
= [tex]2(24\times8+8\times14+24\times14)[/tex]
= [tex]2(192+112+336) =2\times640[/tex]
= [tex]1280 sq. inches[/tex]
Hence,
The surface area of the box is [tex]1280 sq. inches[/tex].
