PSLESix identical rectangular boxes can be stacked into a cupboard 1.2 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 49 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 = 1.2 m
1 m = 100 cm
1.2 m = 120 cm
Width of one rectangle box
= 120 ÷ 2
= 60 cm
Length of the box = 1 u
Height of Figure A = 3 u + 49
Height of Figure B = 1 u + 4 x 60 + 7
The height of Figure A is equal to the height of Figure B.
3 u + 49 = 1 u + 4 x 60 + 7
2 u + 49 = 247
2 u = 247 - 49
2 u = 198
1 u = 198 ÷ 2 = 99
Width of the gap at the side of the cupboard
= 120 - 99
= 21 cm
= 0.21 m
(b)
Height of the cupboard
= 3 x 99 + 49
= 297 + 49
= 346 cm
= 3.46 m
Answer(s): (a) 0.21 m; (b) 3.46 m