Question

The ratio of the length to the width to the height of a rectangular box is 12:4:7. The sum of the length and the width is 32 inches. Find the surface area of the box.

Answer 1

The surface area of the box is
`1280 sq. inches`.

Explanation:

Given that,

Ratio of the length to the width to the height of a rectangular box is
`12:4:7.`

The sum of the length and width of box is
`32.`

From the question,

Dimension of Rectangular box are
`Length (l),\ Width (w) , Height (h)`.

Let the side of rectangular box is x.

`length = 12x\\\\width = 4x\\\\Height = 7x`

Now, Sum of length and width is
`32`
`inches`

Then,
`12x+4x=32`

⇒
`16x=32`

⇒
`x=(32)/(2) = 2\\`

Here we get the dimensions are,

`length = 12x=24inches\\width = 4x=8inches\\Height = 7x=14inches`

Then, surface Area of rectangular box =
`2(lw+wl+ hl)`

=
`2(24*8+8*14+24*14)`

=
`2(192+112+336) =2*640`

=
`1280 sq. inches`

Hence,

The surface area of the box is
`1280 sq. inches`.