PSLESix identical rectangular boxes can be stacked into a cupboard 0.8 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 37 cm gap at the top. The second one in Figure B leaves a 7 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 = 0.8 m
1 m = 100 cm
0.8 m = 80 cm
Width of one rectangle box
= 80 ÷ 2
= 40 cm
Length of the box = 1 u
Height of Figure A = 3 u + 37
Height of Figure B = 1 u + 4 x 40 + 7
The height of Figure A is equal to the height of Figure B.
3 u + 37 = 1 u + 4 x 40 + 7
2 u + 37 = 167
2 u = 167 - 37
2 u = 130
1 u = 130 ÷ 2 = 65
Width of the gap at the side of the cupboard
= 80 - 65
= 15 cm
= 0.15 m
(b)
Height of the cupboard
= 3 x 65 + 37
= 195 + 37
= 232 cm
= 2.32 m
Answer(s): (a) 0.15 m; (b) 2.32 m