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 43 cm gap at the top. The second one in Figure B leaves a 7 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 + 43
Height of Figure B = 1 u + 4 x 65 + 7
The height of Figure A is equal to the height of Figure B.
3 u + 43 = 1 u + 4 x 65 + 7
2 u + 43 = 267
2 u = 267 - 43
2 u = 224
1 u = 224 ÷ 2 = 112
Width of the gap at the side of the cupboard
= 130 - 112
= 18 cm
= 0.18 m
(b)
Height of the cupboard
= 3 x 112 + 43
= 336 + 43
= 379 cm
= 3.79 m
Answer(s): (a) 0.18 m; (b) 3.79 m