PSLE
Six identical rectangular boxes can be stacked into a cupboard 0.9 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 35 cm gap at the top. The second one in Figure B leaves a 9 cm gap at the top and another gap at the side.

1. In the arrangement shown in Figure B, what is the width of the gap at the side in m?
2. What is the height of the cupboard in metres?

(a)
Cupboard width = 0.9 m

1 m = 100 cm
0.9 m = 90 cm

Width of one rectangle box
= 90 ÷ 2
= 45 cm

Length of the box = 1 u

Height of Figure A = 3 u + 35
Height of Figure B = 1 u + 4 x 45 + 9

The height of Figure A is equal to the height of Figure B.

3 u + 35 = 1 u + 4 x 45 + 9
2 u + 35 = 189
2 u = 189 - 35
2 u = 154

1 u = 154 ÷ 2 = 77 

Width of the gap at the side of the cupboard
= 90 - 77
= 13 cm
= 0.13 m

(b)
Height of the cupboard
= 3 x 77 + 35
= 231 + 35
= 266 cm
= 2.66 m

Answer(s): (a) 0.13 m; (b) 2.66 m