PSLESix identical rectangular boxes can be stacked into a cupboard 0.5 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 42 cm gap at the top. The second one in Figure B leaves a 6 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 = 0.5 m
1 m = 100 cm
0.5 m = 50 cm
Width of one rectangle box
= 50 ÷ 2
= 25 cm
Length of the box = 1 u
Height of Figure A = 3 u + 42
Height of Figure B = 1 u + 4 x 25 + 6
The height of Figure A is equal to the height of Figure B.
3 u + 42 = 1 u + 4 x 25 + 6
2 u + 42 = 106
2 u = 106 - 42
2 u = 64
1 u = 64 ÷ 2 = 32
Width of the gap at the side of the cupboard
= 50 - 32
= 18 cm
= 0.18 m
(b)
Height of the cupboard
= 3 x 32 + 42
= 96 + 42
= 138 cm
= 1.38 m
Answer(s): (a) 0.18 m; (b) 1.38 m