### Chapter 5: Algebra... Different "Faces" of Algebra (III)

The perimeter of a rectangle is (6x + 5y) cm.
Suggest 2 possible dimensions of the rectangle.

e.g.
Length of rectangle = 2x + 2y cm
Breadth of rectangle = x + 0.5y cm
Check:
Perimeter = 2 (2x + 2y) + 2 (x + 0.5y) cm
= 4x + 4y + 2x + y cm
= 6x + 5y cm

1. Length of rectangle = 2x + 2.25y cm
Breadth of rectangle = x + 0.25y cm
Check:
Perimeter = 2 (2x + 2.25y) + 2 (x + 0.25y) cm
= 4x + 4.5y + 2x + 0.5y cm
= 6x + 5y cm

- Looi Chi Han

2. Length of rectangle: (3x) cm
Check:
Perimeter = 2(3x) + 2(2.5y)
=6x + 5y cm

Length of rectangle: (2x+2y) cm
Check:
Perimeter = 2(2x+1x) + 2(2y+0.5y)
=2(3x) + 2(2.5y)
=6x + 5y cm

3. -1st Solution
Possible Length of Rectangle: 2x + 2.5y cm
Possible Breadth of Rectangle: x cm
Check: 2(2x+2.5y+x)=6x+5y cm

-2nd Solution
Possible Length of Rectangle: 2x cm
Possible Breadth of Rectangle: x+2.5y cm
Check: 2(2x+x+2.5y) cm

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5. first possible ans:Length: 2x+1y
Check:2x+1y+1x+1.5y=3x+2.5
ans*2=6x+5y

second possible ans: Length:1.5x+2y

Check:1.5+2y+1.5x+0.5y=3x+2.5
ans*2=6x+5y

Check: 2(0.5x)+2(2.5x+2.5y)=6x+5y

Check: 2(0.25x)+2(2.75x+2.5y)=6x+5y

7. 1) Length: 6x, Breadth: 5y
Check: 6x + 5y = 6x+5y

Check: 5y + 6x = 5y+6x
= 6x+5y

(If you do not accept 2), 3) Length: 2x+3y, Breadth: 4x+2y
Check: 2x+3y+4x+2y= 6x+5y

8. This comment has been removed by the author.

9. 1)Length = Breadth = (6x + 5y)/4cm
= (1.5x + 1.25)cm

2)Length = (2x + 1.5y)cm

Check: 1) (1.5x + 1.25)cm * 4 = (6x + 5y)cm
2) (2x + 1.5y)cm * 2 + (x + y)cm * 2 = (6x + 5y)cm

10. 1) Length 2x+1.5y Breadth= x+1y
check: (2x+1.5y)+(2x+1.5y)+( x+1y)+( x+1y) = 6x+5y
3x+3x+2.5y+2.5y=6x+5y

11. The perimeter of a rectangle is (6x + 5y) cm.
Suggest 2 possible dimensions of the rectangle.

L: 3x
B: 2.5y

L+B: 1.5x+1.25y

12. Length of rectangle = 1.5x + 1.5y cm
Breadth of rectangle = 1.5x + y cm
Check:
Perimeter = 2 (1.5x + 1.5y) + 2 (1.5x + y) cm
= 3x + 3y + 3x +2y cm
= 6x + 5y cm