PSLESix identical rectangular boxes can be stacked into a cupboard 0.6 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 42 cm gap at the top. The second one in Figure B leaves a 12 cm gap at the top and another gap at the side.
- In the arrangement shown in Figure B, what is the width of the gap at the side in m?
- What is the height of the cupboard in metres?
(a)
Cupboard width = 0.6 m
1 m = 100 cm
0.6 m = 60 cm
Width of one rectangle box
= 60 ÷ 2
= 30 cm
Length of the box = 1 u
Height of Figure A = 3 u + 42
Height of Figure B = 1 u + 4 x 30 + 12
The height of Figure A is equal to the height of Figure B.
3 u + 42 = 1 u + 4 x 30 + 12
2 u + 42 = 132
2 u = 132 - 42
2 u = 90
1 u = 90 ÷ 2 = 45
Width of the gap at the side of the cupboard
= 60 - 45
= 15 cm
= 0.15 m
(b)
Height of the cupboard
= 3 x 45 + 42
= 135 + 42
= 177 cm
= 1.77 m
Answer(s): (a) 0.15 m; (b) 1.77 m