For a given box, the height measures 7m. If the length of the rectangular base is 2m 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

IF "lateral area" refers to one of the sides, length times height, then Lh = 7L = 84 and L= 84/7 = 12 m

W = 10 m. Then the dimensions are 10 x 12 x 7 m

IF "lateral area" refers to the side area of Wh then 7W = 84 and W=12 with L=14. then

dimensions are 12 x 14 x 7 m

IF "lateral area" means the area of the base, LW=84, then (W+2)W = 84 and

W^2+2W = 84

W+2W+1 = 84+1 = 85

(W+1)^2 = 85

W = -1 + sqr85 = -1 + about 9.22

W = 8.22

L =10.22

then dimensions are 7 x 8.22 x 10.22 m. This last interpretation has the merit that

it requires some math to solve it. But it leads to an irrational fraction for the length & width.

The integer solutions are often intended when the problem is designed. Use of "L" for the lateral

base may suggest it refers to length times height. IF so, the Lh side may be intended. Then

the "best" solution might be Lh=84, with 12 x 10 x 7 m as the dimensions.