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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.

1 Answer

3 votes

Answer:

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.

User Jim Dagg
by
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