Rectangular base

Question

For a given box, the height measures 6 m. If the length of the rectangular base is 2 m greater than the width of the base and the lateral area L is 96 m², find the dimensions (in meters) of the box.

Answer 1

Width = x

Length = x + 2

Height = 6

lateral area = base perimeter * height

base perimeter = 2 * width + 2 * length = 2x + 2(x+2) = 4x + 4

lateral area = (4x + 4)6 = 24x + 24

lateral area given as 96

24x + 24 = 96

24x = 72

x = 3

width = 3

length = 5