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 49 cm gap at the top. The second one in Figure B leaves a 11 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 + 49
Height of Figure B = 1 u + 4 x 55 + 11
The height of Figure A is equal to the height of Figure B.
3 u + 49 = 1 u + 4 x 55 + 11
2 u + 49 = 231
2 u = 231 - 49
2 u = 182
1 u = 182 ÷ 2 = 91
Width of the gap at the side of the cupboard
= 110 - 91
= 19 cm
= 0.19 m
(b)
Height of the cupboard
= 3 x 91 + 49
= 273 + 49
= 322 cm
= 3.22 m
Answer(s): (a) 0.19 m; (b) 3.22 m