PSLESix identical rectangular boxes can be stacked into a cupboard 1.4 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 32 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 = 1.4 m
1 m = 100 cm
1.4 m = 140 cm
Width of one rectangle box
= 140 ÷ 2
= 70 cm
Length of the box = 1 u
Height of Figure A = 3 u + 32
Height of Figure B = 1 u + 4 x 70 + 6
The height of Figure A is equal to the height of Figure B.
3 u + 32 = 1 u + 4 x 70 + 6
2 u + 32 = 286
2 u = 286 - 32
2 u = 254
1 u = 254 ÷ 2 = 127
Width of the gap at the side of the cupboard
= 140 - 127
= 13 cm
= 0.13 m
(b)
Height of the cupboard
= 3 x 127 + 32
= 381 + 32
= 413 cm
= 4.13 m
Answer(s): (a) 0.13 m; (b) 4.13 m