PSLESix identical rectangular boxes can be stacked into a cupboard 0.7 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 34 cm gap at the top. The second one in Figure B leaves a 10 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 = 0.7 m
1 m = 100 cm
0.7 m = 70 cm
Width of one rectangle box
= 70 ÷ 2
= 35 cm
Length of the box = 1 u
Height of Figure A = 3 u + 34
Height of Figure B = 1 u + 4 x 35 + 10
The height of Figure A is equal to the height of Figure B.
3 u + 34 = 1 u + 4 x 35 + 10
2 u + 34 = 150
2 u = 150 - 34
2 u = 116
1 u = 116 ÷ 2 = 58
Width of the gap at the side of the cupboard
= 70 - 58
= 12 cm
= 0.12 m
(b)
Height of the cupboard
= 3 x 58 + 34
= 174 + 34
= 208 cm
= 2.08 m
Answer(s): (a) 0.12 m; (b) 2.08 m