### 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. 1)Length:3x

2)Length:(6x+4y)

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3. Length of rectangle = 3x + 2y cm
Breadth of rectangle = 1/2y cm

Check:
Perimeter = 2(3x+2y) cm + 2(1/2y) cm
= 6x cm + 4y cm + 1y cm
= 6x + 5y cm

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5. 1)
Length:6x cm

Check: (6x+5y)cm

2) Length: (3x+ 3y)cm

Check:(3x+ 3y)+ (3x+2y)cm=(6x+ 5y)cm

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

2) Length: 3x+1y cm
Check: 2(3x+1y)cm+2(1.5y)cm=(6x+2y+3y)cm=(6x+5y)cm

7. 1)Length:2x+1.5y cm
Check:[(2x+x)*2]+[(1.5y+y)*2]
=(3x*2)+(2.5y*2)
=(6x+5y)cm
2)Length:x+2.5y cm
check:[(2x+x)*2]+(2.5y*2)
=(3x*2)+5y
=(6x+5y)cm

8. 1 : Length = 3x
Check = 2(3x) + 2(2.5y) = (6x+5y) cm

2 : Length = 3x + 1.5y
Check = 2(3x+1.5y) + 2(1y)
= 6x + 3y + 2y
= (6x + 5y) cm

9. 1) Length-> (3x + 2y) cm

Check:
Perimeter-> 2(3x+2y) cm + 2(1/2y) cm
= 6x cm + 4y cm + 1y cm
= (6x + 5y) cm

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

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

-Owen

Check:2(3X+2.5Y)CM=(6X+5Y)CM

2.Length-2.5XCM+0.5YCM
Check:2(2.5X+0.5Y)CM+2(0.5X+2Y)CM=(6x+5y)CM

12. 1) Length : (3x)cm
Check : 2(3x+2.5y)cm=(6x+5y)cm

2) Length :(2.5x)cm+(2y)cm
Check :2{[(2.5x)cm+(2y)cm]+[(1/2x)cm+(1/2x)cm]}=(6x+5y)cm

13. 1.
Length: 2x + 1.5y cm
check: Perimeter: 2(2x + 1.5y cm )+2(1x+ 1y cm )
= 4x+3y cm+2x+2y cm
=6x +5y cm

2.
Length; 1.5x + 1.5y cm
check: Perimeter: 2( 1.5x + 1.5y cm)+2(1.5x + 1y cm)
=3x+3y cm+3x+2y cm
=6x+5y cm

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15. Possibility 1:

Length of rectangle = x + y cm
Breadth of rectangle = 2x + 1.5y cm

Check:
Perimeter = 2(x + y)+2(2x + 1.5y)
= 2x + 2y + 4x + 3y
= 6x + 5y

Possibility 2:

Length of rectangle = x + 0.5y cm
Breadth of rectangle = 2x + y cm

Check:
Perimeter = 2(x + 0.5y)+2(2x + y)
= 2x + 1y + 4x + 2y
= 6x + 5y

16. 1) Length: 1.75x km + 1y
Check: Perimeter: 2(1.75x + 1y) + 2(1.25x + 1.5y)
= 3.5x + 2y + 2.5x + 3y
= 6x + 5y
2) Length: 2x + 0.5y
Check: Perimeter: 2(2x + 0.5y) + 2(1x + 2y)
=4x + 1y + 2x + 4y
=6x + 5y

17. [1] Length: x + 2y
Check:
Perimeter= 2(x + 2y) + 2(2x + 0.5y)
=2x + 4y + 4x + 1y
=6x + 5y

[2] Length: 1.5x + 1y
Check:
Perimeter= 2(1.5x + 1y) + 2(1.5x+1.5y)
=3x + 2y + 3x + 3y
=6x + 5y

18. 1. Length = 2x + 2y
Perimeter = (2x + 2y + 1x + 0.5y) * 2
=6x + 5y

2. Length = 2.5x + 1y
Perimeter = (2.5x + 1y + 0.5x + 1.5y) * 2
=6x + 5y

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

20. Length: 1x+2y cm
Perimeter: 2(1x+2y) + 2(2x+0.5y)cm
=2x +4y=4x=1y cm
=6x + 5y cm

21. 1) Length: 3x
Check: [2(3x)]+[2(2.5y)]
= 6x+5y

2) Length: y+2x
Check: 2(y+2x)+2(1.5y+x)
= 2y+4x+3y+2x
=5y+6x

22. Mark :) :( :&#39;( (^^^) :D :O :42: O:) :p 3:)4/21/2011 08:31:00 AM

1) Length:( 2.5x + y)
Perimeter: 2(2.5x + y) + 2(x/2 + 1.5y)
= 5x + 2y + x + 3y
= (6x + 5y)

2) Length: (2x + 4y)
Perimeter: 2(2x + 4y) + 2(x - 1.5y)
= 4x + 8y + 2x - 3y
= (6x + 5y)

23. Length of rectangle : ( 2x+1.5y)
Perimeter of rectangle: ( x+y)

Check :
Perimeter = 2(2x+1.5y) + 2(x+y)cm
= 4x + 3y + 2x + 2y cm
= 4x + 2x + 3y + 2y cm
= 6x + 5y cm

24. Length:3x