SOLID MENSURATION QUESTION I FAILED TO ANSWER BUT DIDN'T KNOW THE SOLUTION

Question

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 96 m², find the dimensions (in meters) of the box.

Answer 1

Let w,h,l be the width, height, and length of the box

Given h =3m, l = w+2

Lateral Surface area = 2( h x w) + 2 (h x l)

= 2h (l + w)

Substitute l= w+2, h =3

= 2*3(w+w+2)

= 6(2w+2)

=12w +12

Given L = 96 m^2

12w +12 =96

12w=84

w = 7,

l= w+2

l=9

Dimensions of the box are height =3m, length =9m, width =7m

Answer 2

Let w= width of bottom then l = length of bottom =w+2. The area of a face is then 3w=96 yielding w=32 and l=34. The volume is then 3*32*34= 3264 m³