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 50 cm gap at the top. The second one in Figure B leaves a 8 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 + 50
Height of Figure B = 1 u + 4 x 40 + 8
The height of Figure A is equal to the height of Figure B.
3 u + 50 = 1 u + 4 x 40 + 8
2 u + 50 = 168
2 u = 168 - 50
2 u = 118
1 u = 118 ÷ 2 = 59
Width of the gap at the side of the cupboard
= 80 - 59
= 21 cm
= 0.21 m
(b)
Height of the cupboard
= 3 x 59 + 50
= 177 + 50
= 227 cm
= 2.27 m
Answer(s): (a) 0.21 m; (b) 2.27 m