PSLESix 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 47 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 = 0.9 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 + 47
Height of Figure B = 1 u + 4 x 45 + 7
The height of Figure A is equal to the height of Figure B.
3 u + 47 = 1 u + 4 x 45 + 7
2 u + 47 = 187
2 u = 187 - 47
2 u = 140
1 u = 140 ÷ 2 = 70
Width of the gap at the side of the cupboard
= 90 - 70
= 20 cm
= 0.2 m
(b)
Height of the cupboard
= 3 x 70 + 47
= 210 + 47
= 257 cm
= 2.57 m
Answer(s): (a) 0.2 m; (b) 2.57 m