For a given box, the height measures 3 m. If the length of the rectangular base is 2 m greater than the width of the base and the lateral area L is 84 m2, find the dimensions (in meters) of the box.

Question

length ___ m?

width __ m?

Answer 1

This problem may be ambiguous, depending on what "lateral area" means

It can mean one of 3 things:

He're's one interpretation, that at least requires some math.

Assuming "lateral area" refers to the base of the box

L=2+W

84=LW = (2+W)W = 2W +W^2

W^2 + 2W = 84

W^2 +2W + 1 = 84+1

(W+1)^2 = 85

W +1 = sqr85

W = sqr85 - 1 = about 8.22 m

L = about 10.22 m

dimensions are 8.22 x 10.22 x 3 m

Here's another interpretation, where "lateral area" means one of the sides. But it could mean the side with length by height, or it could mean width by height.

the following is length by height:

Lxh= Lh=84 = (2+W)3 = 84

6+3W =84

3W =84-6 = 78

W=78/3 = 26

L= 31

then the dimensions are 26 by 31 by 3 m

Last interpretation is that "lateral area' refers to width times height

3W = 84

W =84/3 = 28

L=28+2 = 30

the the dimensions of the box are 28 by 30 by 3 m

Use of "L" for the lateral area might seem to refer to L x h as the area intended

so 26 x 31 x 3 m might be the likely dimensions

the last 2 interpretations have integer solutions which suggests they might be the intended solution, rather than an irrational fraction.

But sometimes problems get miscopied, and it is difficult to tell what solution may be "best"