PSLESix identical rectangular boxes can be stacked into a cupboard 1.3 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 8 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 = 1.3 m
1 m = 100 cm
1.3 m = 130 cm
Width of one rectangle box
= 130 ÷ 2
= 65 cm
Length of the box = 1 u
Height of Figure A = 3 u + 32
Height of Figure B = 1 u + 4 x 65 + 8
The height of Figure A is equal to the height of Figure B.
3 u + 32 = 1 u + 4 x 65 + 8
2 u + 32 = 268
2 u = 268 - 32
2 u = 236
1 u = 236 ÷ 2 = 118
Width of the gap at the side of the cupboard
= 130 - 118
= 12 cm
= 0.12 m
(b)
Height of the cupboard
= 3 x 118 + 32
= 354 + 32
= 386 cm
= 3.86 m
Answer(s): (a) 0.12 m; (b) 3.86 m