PSLESix identical rectangular boxes can be stacked into a cupboard 1.3 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 31 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.
- 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 = 1.3 m
1 m = 100 cm
1.3 m = 130 cm
Width of one rectangle box
= 130 ÷ 2
= 65 cm
Length of the box = 1 u
Height of Figure A = 3 u + 31
Height of Figure B = 1 u + 4 x 65 + 9
The height of Figure A is equal to the height of Figure B.
3 u + 31 = 1 u + 4 x 65 + 9
2 u + 31 = 269
2 u = 269 - 31
2 u = 238
1 u = 238 ÷ 2 = 119
Width of the gap at the side of the cupboard
= 130 - 119
= 11 cm
= 0.11 m
(b)
Height of the cupboard
= 3 x 119 + 31
= 357 + 31
= 388 cm
= 3.88 m
Answer(s): (a) 0.11 m; (b) 3.88 m