Question

3. The length of a box is 5 m longer than the width, and the height is 3 m shorter than the width. The volume of the prism is 100 ml. Determine the possible dimension(s) of the box. A complete algebraic solution and analysis is required for full credit.

Answer 1

Jue 3. solution. Let width of of a box (6) = x Given that length of a box is than the width and and height is than the width then , longer 3 m shorter M + 5 length (1) height (6) H-3 Since = 100 m3 :-) volume of prism (box) l.wih = 100 (x+5).1. (01-3) = 100

- 100 =0 x (312-381 + 5-15) = 100 73 +2712-15 r - 100 713 5 12 + 7 x2 35 n +2ox 72 ( 71-5)+7( 2-5) + 20 ( 74-5) = 61-5) (42+7+4 + 20 ) - 7 + 749-100 755 00 2 r -7 + 451 ie. N=5 2 - So for real valued solution, N = 5 e = 5+5 - 10 (l= 31+5) 5-3 = 2 b n-3 Therefore possible dimension of the box , width of box 5 m 10 m length of box height of box 2 m