PSLESix identical rectangular boxes can be stacked into a cupboard 1.1 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 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 = 1.1 m
1 m = 100 cm
1.1 m = 110 cm
Width of one rectangle box
= 110 ÷ 2
= 55 cm
Length of the box = 1 u
Height of Figure A = 3 u + 42
Height of Figure B = 1 u + 4 x 55 + 10
The height of Figure A is equal to the height of Figure B.
3 u + 42 = 1 u + 4 x 55 + 10
2 u + 42 = 230
2 u = 230 - 42
2 u = 188
1 u = 188 ÷ 2 = 94
Width of the gap at the side of the cupboard
= 110 - 94
= 16 cm
= 0.16 m
(b)
Height of the cupboard
= 3 x 94 + 42
= 282 + 42
= 324 cm
= 3.24 m
Answer(s): (a) 0.16 m; (b) 3.24 m